i think it is a capacitor too and the + is just to allow the assemblers to know polarity. the + is on pcb next to the silver leg that comes out the side.
hot is not good. i cannot follow the traces to it from your picture. they covered the top with goop so no way to know the part number either.
when you look at the legs and how they attach to the traces. do all the legs go into one trace that is wide and connects almost all the legs on one side or do they run off separately?
if you can, move the light so there is not so much reflection and get a close up picture showing the traces there we might be able to identify what it does. 18 pins is more than a voltage regulator though. maybe the traces will help identify it.
but while the fuse is out we can try to measure those mosfets too, with the diode tester. there are four of the them labeled Q1-Q4 with two on each side. there is a wide trace running up to and underneath them. you can see where they have test points labeled that allow you to put the probe of the voltmeter into the trace through the shellac covering everything.
i think the TP1 is the drain of the output mosfets. so use the diode tester function on your voltmeter to test. it sends out a small 1A voltage and if the red probe is on the anode of the diode and the black probe is on the cathode then the current will flow through the diode and you can read the diode forward bias in millivolts.
a diode conducts in one direction so if you see a diode forward bias it will be in the range of 200-500mV. that would mean the diode is conducting. if you reverse the probes then the diode should show open circuit and meter will be off scale.
if the diode is shorted, or if you are measuring a wire that conducts then it will appear as 0V or very low volts.like 01 or similar. make sense?
so those four mosfets have a drain and source leg. the body diode of an nchannel mosfet conducts when the red probe is on the source leg and the black probe is on the drain leg. when you measure the body diode in the mosfet you can tell if the mosfet is still ok or has shorted out.
those wide traces carry the current to the mosfets from the battery and then out to the motor, and one trace is connected to the source of the mosfet and the other connected to the drain. i think TP1 is on the drain of the output mosfet.
so put the red probe on the TP1 and the black probe on the black wire to the motor controller. you can put the probe right on the pin in that black plug, the pin that is on the black wire. it should read 0V if that is the drain of the mosfets since the drain is always connected to the motor. if it is open then that means that the TP1 is not on the drain of the output mosfet. if it reads 0V then that means the TP1 is connected to the motor negative, as it should be.
then do the same with the other test points on the other side of the mosfets. TP1 to TP19 and TP1 to that round circle exposed under TP302 and each of the circles underneath it. it is hard to keep track of all the numbers i know, but what we are trying to do is see if those mosfets have blown open when you had the plug problem, or if they have done something that causes the IC to get hot. if they burned open then they will read off scale.
it may be normal for it to be hot if it is a voltage regulator, and the current would be the circuit current coming out of it to drive the BMS circuitry.
i know this is a lot to take in so quick so don't be spooked and as long as the fuse is removed, the battery voltage will not damage your meter.
you can also do the diode test between the black wire to the battery and the TP1 and the others too. kinda just go through all of them to get a feel for what you are measuring as you go along, and there may be other test points on the front i cannot see which you would wanna do the same thing to. this is all just to see if we can find a burned open mosfet that is preventing the current flow to the motor from the battery.
yep i know, lotta hassle, and spooky because it is unfamiliar, but it may help isolate what happened.
actually i am hoping you find an open circuit in the wiring to the plug when you are testing it, and that the mosfets will be ok. but since i don't know how or what was shorted there is no way to know yet. if the mosfet has the voltage reversed and a lotta current flows then it coulda been damaged.
lotta yakking, but i hope it helps a little. take your time and don't get flustered. you have done a lot more than most people here ever do to find the problem. and this circuit is hard too.