So funny you mentioned a "mouse" - So I noticed when I uncovered her after the winter, I keep a trickle charger on the battery, and noticed some mouse droppings on the top of the battery. So I definitely had a mouse trying to keep warm on the battery at some point.
I would try a "wiggle" test on the main harness while it is running, even though it is not acting up right now. The fact that you have evidence of mice in the engine bay, there is a possibility they started chewing on wires. Doesnt hurt to check.