Congrats on the purchase and welcome! No that's not normal.
First place I would look is the condition of the 9-way connector going to the LH switch block. It is absolutely common for these to melt, since they run one phase of unregulated alternator power up through a second pole in the light switch. The plug is usually mostly damaged around the two wires in question, however the heat involved can damage other nearby wires or cause high resistance joints. Many disable this loop and run all three phases direct to the regulator (may require upgraded regulator, they switched out one phase to prevent overcharging the battery when little electrical load was present).
Other obvious thing with those symptoms would be a bad earth. Make sure you have a good earth going up into the fairing harness, disassemble, clean and refit any earth points and check they are good. It's a decent harness that works well when all in good condition, but like anything can be improved. Inserting a dedicated earth wire from the main earth point to that point near the coils is not a bad thing at all. Also check the earth into the LH switch block, from memory there is an actual earth wire in the switchgear harness itself, but no corresponding wire in the chassis harness instead relying on grounding the switchblock through the handlebars/steering head bearings. I'm pretty sure I've added a wire back to the earth point near the coils to properly earth that. Apologies if I have misremembered that bit, it's decades since I have done those sort of little things on my bikes.
If you're getting onto Marty as a mechanic in Sydney, he will know all this stuff and be able to rectify/enhance as required.