Have been following your project, coming along good.
No way to check water pump, it either works or it doesn't. I would check the thermostat first, take it out and check it.
Coolant won't go bad, but additives may become less effective with time. Shouldn't affect the engine temperature either way. I'd change out the coolant.
May want to take the rad and have it cleaned - lots of crud can build up after 33 years. The rads on the 1200 are smaller than the 1000/1100, and just large enough to provide good cooling at highway speeds. When you operate in town, stop/go or heavy traffic, engine temp will rise, but returns to normal after a short stint back at highway speeds. Honda called it a high efficiency rad. It was good the fan came on, that circuit is working.
I thought I had cooling issues after I installed an external alternator. Went through everything, including a new rad core. Here are some pictures of the old rad core ends. No internal pictures of course but when I inspected the core, there was significant reduction in the passages. The fellow that did the work, been at it for many years, estimated a 30 to 40 percent internal flow reduction.
I have removed the aftermarket rad cover. I measured the air restriction from the aftermarket grill and found it to reduce the cooling area by about 18%, a significant amount for a cooling system that is just large enough for the 1200. I have been operating the bike with no rad cover (the OEM is just a mesh that might stop extra big bugs). I think this is helping a lot as well. Here are some pics of the OEM and aftermarket rad grills. The after market rad grill has 17 slats that 1/8" by 10". The rad size is 10" by 11". Aftermarket Grill:
I'm riding my 1200 here in Victoria, temps in the 5 to 10 deg C range. Takes a while to get to operating temp, but after it does, riding in town - stop/go, the engine temp does rise. At these temperatures, the engine will still heat up at idle such that the fan will come on.
RPM for the 1200 is 1000 +/- 100 RPM.
Just a few thoughts.
Do you have the 1200 OEM service manual, or the electrical troubleshooting manual? Have these in PDF - large file - can send by wetransfer but need email. Pm if you would like me to send.
Cheers