You should be using a 10w40 oil in it.
It's possible the oil pressure sender is out-of-spec (light is supposed to go out at 3-5 psi / 0.20-0.35 bar), pressure spec on a 1500 with hot engine and 10w40 oil at idle is 11 psi / 0.75 bar, the 1200 should be similar. Oil pressure senders in these bikes rarely go bad, but is not unheard of. See if you can get a hold of an oil pressure gauge to connect to the engine, might be able to get loaner gauge from autoparts store. If not, I don't think a replacement sender will cost that much.
A note on Oil Pressure sender threaded pressure fitting - US made vehicles use NPT threads, Honda cars (and Motorcycles) use BSPT threads, the fittings are pretty much the same size but the thread pitch is different (24 pitch vs 25). If you are threading your oil pressure gauge into the engine and notice the threads starting to bind, don't tighten it down, it could bugger up the threads. See if there's a NPT/BSPT thread adapter in the pressure tester kit.
Having said that, an oil pressure sender for a Honda Car should work just fine if you have a hard time finding OEM part.