My experience unless the chase boat is already out or near ready to leave for another boat in your area. You will not see the chase boat until the next day. The reality on the dock is there is no crew and hoard of spares just sitting like fireman back at the base ready to run to your fix. The call for a chase boat goes into the que with everything else. In most cases the charter guests at the base dock will be cared for first and sent on their charter before the chase boat crew is free to come out and work your issue.
Unless you are talking to a leader on the dock via a cell telephone. You are likely just getting lip service from a the desk staff that is not in loop of the work orders at hand. I would also not expect anyone at the base to tell you to operate a boat you called in and reported unsafe. So the message back is sit there; we will send someone out.
With four decades of chartering. I would never plan my day around a chase boat. Just communicate to the dock and operations manager where the boat will be and how they can get into it or go back to the dock when the time is good for you. If any of this is important to you. Get the cell number from the person running the dock before you leave.
Once you detail a problem. The parts must be found, the tools must be found, a multi person crew must be freed up with a chase boat to travel to you, complete the repair, and then return to the base before end of the work day. That is much more complicated in reality that any brochure produced by a marketing team in a windowless conference room.
If a sleep aboard is not possible? That means the turnaround is really pressed with great chance the issues from the last trip and maybe many trips before will not be addressed. We will not take a boat we cannot sleep on and inspect the night before and morning of giving us and the crew all day to address any issues. Rushing away from the dock or rental boat turnarounds never ends well.