A sucking test is the opposite of "
pressure test." Your system needs a pressure test, not a suction test. What needs to be known is still not known ... does your system hold pressure ???
I believe many parts stores lend out cooling system pressure tester kits that have the correct adapters. Do a low and high pressure test. A low is 6-8 lbs and a high is 16-20 lbs. Do each test for at least 4 hours. Often if our system has a leak, the leak first pools before spilling into another void to pool, before the first drop will finally spill over and hit the pavement. According to Honda's maintenance schedule, a pressure test needs done every 8,000 miles. Assume nothing and don't forget to test your new cap.
It's been my experience, that overheating is usually due to poor maintenance. Hopefully your Wing got its coolant changed in 2009, 2011, 2013, 2015 and in 2017 (or every 24k whichever comes first). Basically, it should at least be on it's 5th coolant change. I've pulled engines down for tranny repair and the outer walls of their cylinders walls (also known as coolant jackets) are coated with a white substance that does not come off from hot tanking, carb cleaner, or BrakeClean. It probably something that happens from electrolyses (from old coolant). Since such coating probably reduces heat from it transferring from the cylinder walls and into the coolant, I'm sure their cooling system will forever be less effective. At the least, it slows the movement of coolant in a critical area.
As for pulling the OEM fuel tank. No, the battery box does not need to be removed. Usually I will removed the battery bracket bolt, and screw back in the bolt 2 threads to keep the collar in the box from dropping out of its bolt hole. It's easiest if the tank is less then 1/4 full.
Just an FYI ... I stock 3 thermostats and in the 10 years of repairing probably more GL1800 then any other shop, have never sold even one of them; I doubt you have a bad thermostat. If your water pump is bad, it is because it is leaking or it sounds like this
http://www.triketalk.com/forum/threads/42705-Water-pump-noise
If you think your water pump has a different noise, confirm it by listening to it with a rubber hose touching the pump and the other to your ear.
Also, a cooling system inspection includes inspecting the recovery system. Be sure to remove the reservoir tank and inspect the nipple end of the hose that goes into the tank. Any cracks around it, or any cracks on the other 2 recovery hose ends, and they need replaced. The inspection should include looking at the obvious. Are there any accessories that block air flow passing through the radiator grill area. An efficient system includes no chrome in that area at all. OEM black shield on the front side of the fans, and the outsides of the radiators are acceptable. Everything else should not be there.
Be sure to check your fans. Once they come on, place both hands under the headlamps. You should feel even blow and even heat.