In Revelation 3:21 (NASB), it says,
The one who overcomes, I will grant to him to sit with Me on My
throne, as I also overcame and sat with My Father on His throne.
My understanding of "right hand" is "executive officer", like the president or CEO -- the one who does most of the work, but with oversight from the "owner". Think "right-hand man".
But in the above verse, it is clear that both Jesus and His Father are on the throne together, and since they are two persons of the Trinity which is God, they are in complete unison and harmony, and rule as one "Hear Oh Israel the Lord thy God is One God." -- Deut. 6:4 KJV
This is also based on a confirmation by God himself relayed by a first-person account in the book, "Murdered Heiress, Living Witness" by "Petti Wagner" who has an autobiographical book about her murder and resurrection, and what God taught her about himself on Amazon. This book has forever convinced me 100% that the doctrine of the Trinity is correct, faithful, and true.
So, then, who cares whether Jesus rules, or His Father rules, if they rule together in perfect harmony? In the light of eternity, this is not a question that you really have to worry about.
The final implication of the quoted verse is that we get to rule as well! Wow! What an honor!
The following excerpt from the above-referenced book, occurs after her resurrection (she had been killed by electroshock therapy machine turned up to maximum.)
At nine o'clock, God began to instruct me in His plan for my escape. It was totally absurd for me; all my life, I had based every decision on logic. He knew exactly what I was thinking. In fact, His first words were, "As soon as you learn that I am not confined to logic. As He paused, I felt ashamed of my "rational" thought about saving a knife instead of the spoon from the dinner tray. I silently acknowledged Him. I felt immediate, gentle forgiveness flowing through me. Then the Voice continued: "As soon as you learn that I am not confined to logic, that I am supernatural and super-normal, we can work together."
I wanted to ponder those words, but God said, "Let me show you who We are." He hadn't appeared to me in bodily form as Jesus had while I was in that unearthly sphere. However, I instantly saw a ball of light which totally filled and illuminated the dingy room. "We are One - Father, Son, and Holy Ghost," the Voice announced. Then the bright orb split into three separate balls which formed a triangle. "Now we are separate." I knew, like I had experienced total knowledge while in that other dimension, that God the Father was the shining spherical light at the top of the triangle; Jesus was the one below on His right; and the Holy Spirit on His left. Though They spoke as one, each member of the Trinity was identifiable by His distinctive voice. The Father had a deep, booming voice with resonant overtones like I had never heard before. Jesus' voice was tender and compassionate, just like when we sat in the chairs. The Holy Spirit sounded somewhat like the nicest teacher I ever had - who had taught me law and psychology. "Now We are One again." As God spoke, the three lights merged into a single brilliant mass. The radiance took full possession of the entire room. It was light, but it was also pure love, and it seemed to assume the shape of the space it filled. For a brief moment, I felt an arm enveloping and holding me. Then, just as if a switch had clicked, the light suddenly left the room. The Voices remained, teaching me about God and carefully laying the groundwork for my escape.
It all still seemed so absurd to me, even after all I had experienced during that incredible day. I had so little knowledge of God, of His Word, of His ways. I kept wondering why I had been singled out for all that was happening to me. It was just too much for me to take in. As though my uneasiness and lack of knowledge were understood, the Voices instructed me - separately and together, but always in total agreement and harmony with one another. I could always identify the Person who was speaking, just from the unmistakable sound of His voice. It was the Holy Spirit -the Teacher- who gave the first command. "Tell the guards you have had a rough day and are going to bed early." I laughed out loud. It was like a joke - the understatement of the century. For some reason, God didn't seem to mind that I laughed. I felt like a child, open and innocent and wide-eyed before Him. Though I wasn't in the habit of telling the guards anything, I rose from my bed and knocked on the door to deliver the message. The Follower responded almost most immediately, peering cautiously as he opened the door ajar. "I'm going to bed early, so please don't bother me," I announced, startled at the authority rising in my voice. "I'm very tired." He seemed caught so completely off-guard that I decided to blurt out another question: "Is it possible for me to see Dr. Holmes before I retire?" "No," the Follower stammered," h-h-he left early this afternoon. But I'll tell him ... you want to see him - to see him in the mornin'." He shut the door softly, clicking the dead bolt back in place. I'd never seen a more confused man. I almost felt sorry for him. Almost. As soon as the door was closed, the Lord gave me my next instruction: "Now remove your wig head from its bedside stand, and write on the Styrofoam as I tell you." Each new step seemed more puzzling to me than the last. And I kept wondering if the Follower outside the door was hearing God's voice like I was. I'm sure he hadn't, since he stayed outside the room, but I couldn't understand why. So I took the black wig off the stand, and I wrote a message that God dictated: Dear Dr. Holmes - You may do anything you wish with this head - but leave mine intact. - Dr. Wagner It was as if I was sharing some kind of inside joke with God. I had never thought of Him like that before. He had always been some faraway relic, like many of the religious artifacts I had seen. I was enjoying just being in His presence. Next, God had me place the curly, black wig back on the Styrofoam stand and put it on the bed. Then He showed me exactly how to adjust the pillows below it to resemble my body. In the outlined darkness, it really did look like a person in the bed. "Now, pull the spread up." I smiled at the little details. Since that first hideous day, I had always slept with the blood-stained spread over my head, like a small child hoping that the thin material would keep away my very real boogeymen. "Now, hide behind the curtain," He continued. "At exactly 9:20, the guards will shine a light through the window in the door and think you are fast asleep. They will not make another check tonight." I knew I had to follow every instruction carefully. My life depended upon every word He spoke. The drapes, like the bedspread, were made from drab material designed more for durability than beauty. Still, the drapes were fully lined. I was grateful for the added body and bulk as I hid behind the folds and flattened myself firmly against the window. My nostrils twitched as I stood. I was almost amused at myself, even in the midst of my unfolding life-and-death drama; I stood there wishing I could toss those dusty, foul-smelling drapes into a washing machine until they were fresh and clean again. I made sure that I was completely concealed from the soon-coming gaze of the guards. Even my chic black boots, once shiny, but then caked and stained, were not visible. The years of use had made the drapes sag, even overlapping down on the floor several inches. Once sure that I was as safe as possible, I could do nothing but wait, trying to keep my tense breathing from moving the drapes. I watched the blinking time-and-temperature sign. I hoped it would be the last time I would have to spend the night with my old, continually flashing "friend." As I waited, the Holy Spirit spoke: "Say this after Me -'Lord, I'm one of Your little lost sheep. I've lost my way. Please take me back into the fold.'" What? I thought, "But that's something just like a child would say!" So strange. Nevertheless, I repeated the words. And as I spoke, a rush of power came upon me, so powerful and great. I didn't understand, but I knew there must be some urgent purpose for that surging power. Then I saw the flickering flashlight beam shining briefly through the small window of the locked door. I strained to see the flashing sign across the street. It was 9:20 p.m. Exactly. Just as God had said it would be! Within a split second after the light beam disappeared from the room, Jesus spoke clearly to me: "Now, let us get to work!"
Petti Wagner. Murdered Heiress: Living Witness (Kindle Locations 673-719). Kindle Edition.
While this is not scripture, it is a first-person account, and in my personal judgment is wholly true and reliable.
This also displays well the complete unity of the Trinity that I always imagined, and how they are separate persons, yet a completely unified "God", all at the same time. How wonderful to get this confirmation for myself -- I hope you take it for yourself as well.