Nov 2024 it was announced:
Effective November 1, 2024, single men 40 and older may be called as full-time senior missionaries if they do not have dependent children living at home. Those who serve in this capacity will be considered for various assignments in area and mission offices, family history and other roles for which they have unique life experience (for example, medical, legal and other realms).
Similar to most single senior sisters, single senior elders will be devoted to their individual area of responsibility and will not serve in a companionship. Single senior missionaries, like senior couples, can serve for six, 12, 18 or 23 months.
The senior missionary types can be found here and specific opportunities can be found here.