No, I do not know the LED readouts. Someone here may know. How well charged is the battery? Is that a low battery signal to check voltage?
I'm more curious about that relay heating up. I'm thinking something like: Remove ground battery cable and note sparking/arcing if any> with key off. Tap the ground cable back onto the battery post. With key still off, did you see a tiny orange spark or was it a wide, strong, blue/white spark?
1. For argument sake, say it's with key off, there is no arc present. Beats me guessing the product's setup, but say there is a tiny spark touching the cable to the post. Call it the clock option, the self memory in the black box? Then say with no spark present, no memory saved, no clock memory being saved. No short present.
2. For argument sake, say key on now. Was there a white/blue arc or a tiny orange spark with key on? Was the arc hot enough to melt the lead battery post some? Then, there is your short heating up the breaker. If say the headlight and taillight turn on normally with key on, then there is your hotter spark jump. Take both out of the loop and try again. Same blue/white arc, you haven't found it yet. The short is possibly present with no lights to still cause the arcing.
3. Trans in top gear so it's easier to push, line up crank sensor's rotor so both pins match at the crank sensor. Find N and do not move the pin nipples away from each other. Leave clutch lever alone on a dead engine. Move the bike back and forth to find top gear and N. The free hand off the bar can now be shifted by hand. The plug wires removed, but the rubber caps are just sitting on the plugs so you can hear the spark jump from the cap to the top of the plug. Start to disconnect as much as you can and do not lose 12v to the black box. When you don't see the arc, you found it at the last disconnect you made. So it's key on, meter set to 20v, red probe to key switch... do you have 12v up to the switch going in? Yes? Then it's key on, red probe to the other wires going out from the switch. I'd start there.
4. Other fast checks would be key on, red probe to the coil wires. Is there 12v there? Yes? Then with a flat blade screwdriver, key on, touch both pins at the crank sensor and see if you can hear the arc jump from the steel clip to the plug cap ends. Remember, crank sensor wise, you are the old style points breaker. So if you hold that blade to both pins, you are sending the coil to ground. You have to toggle the pins in other words; as if opening and closing a set of points to see if the crank sensor is bad. So you break away from one pin and then ground that pin again to create a lot of spark to the plugs so as to hear something.