ccoombs This really boils down to the design that was commissioned for you as even the OOTB database doesn’t have time capture in it from my knowledge.
It sounds though someone has put a time field on the Resolution object from your description.
To capture elsewhere before closure you would need to create a collection object to hold these that are then triggered by a manual action in the process wherever you need. In the OOTB we had for our clients I created a “Time Spent” collection. I created itvon the “Process” object too so you could capture from process and task process alike. It even rolls up the total tine etc via calculations.
Unfortunately it is too complex to distill into this post though. I’d suggest talking to whoever designs your system.
There is a content pack that explains how to add time capture based on start and stop of timers too if you are interested in that approach.
For me and IMHO though a lot of this is often added retrospectively so the manual action approach to capture is better than remembering too, or cursing later, that you forgot to start a timer!