How long does it take for a Reserve Unit to find a new AGR or Unit Administrator?

AGR fills will take place according to the Mission Essential Requirements (MER) list. I am just finalizing mine now for my command. This basically rank orders all my projected or actual AGR vacancies on a 1 to n basis and that is what order HRC will fill them. Get with your chain of command to input and let them know you need to be higher priority than other units in your major command. The UA will need to be advertised, but you can do a by name of a Soldier in the unit. If that is the case, you can skip the whole advertising, interviewing, etc. Get with the SSA at your battalion HHC to show you how to do this.

a freakishly long amount of time depending on the mood of the people approving the positions and the budgets.

I would find someone in the unit ASAP to put on orders to do the job until you find someone.

It's not predictable.

Thank you everyone for the comments. Hopefully we will hear something soon.