GFCI outlet trips overnight. The breaker indicates there is ground fault. Outlet tester shows no lights (no power?)
The outlet tester shows no lights, because there is no power until you reset the GFCI.
A GFCI can trip because there is a ground fault or because the GFCI itself is bad. Most of the time, it is an actual ground fault - a life-safety condition. Consider the different possibilities:

The disposal has a fault which only appears after an extended period of time. For example, there could be a very small leak of water into the motor. It could be that it is a very slow leak, so it does not show up on immediate use, but does trip the GFCI after several hours of drip-drip-drip. Then it trips in the middle of the night. By the time you get to it, the water has dried out and you are able to reset the GFCI and use the disposal again for a while. Key question: How old is the disposal? Any signs of cracks in the case? Any water under the sink, anywhere?

A downstream device has a fault. A GFCI can be connected to multiple devices (receptacles or hard-wired) using the LOAD connections. This is unlikely for a disposal receptacle, but it is possible. If that is the case, or if you have something else plugged in to the 2nd receptacle (assuming it is a typical dual receptacle) then a different device could be causing the problem.

Water dripping into the receptacle. A long-shot, but if there is water leaking under the sink and slowly making its way down the cord to the receptacle, that could cause a GFCI trip. If that's the case, you want to to trace back to the disposal, drain and sink to find where water is leaking.


Based on discussion in comments, it is not clear whether the disposal is causing the trip or something else. Suggestion: Next time you use the disposal for the &quot;usual&quot; amount, assuming you have no GFCI trip at the time, unplug it. Then the next morning see if you find:

GFCI tripped before you plug in the disposal. This would indicate a problem with something else on the circuit or with the GFCI breaker itself.
GFCI trips immediately upon plugging in the disposal or after plugging in as soon as you try turning the disposal on. This would indicate a problem in the disposal itself.
Disposal runs fine for a while after plugging it in. This would indicate some sort of leakage inside the disposal causing the &quot;usual&quot; trip and drying out before you plug it in (or on a regular day, drying out before you reset the GFCI).