What kind of turn signal relay to get?

Electronic (electromechanical) flashers operate on varying loads.
you didn't mention LEDs in the topic post. with LEDs I don't know if you need to install anything else, such as a resistor.

You need a HD flasher made for trailer towing. Those will flash the same regardless of load. Don't get a LD one, they will not flash correctly. Also I never had any luck with autozone or the other discount chains. Napa used to sell a decent relay. Can't say for sure if they still sell a decent one. In this day and age, hard to buy a part that actually works.

My relays work fine, I'm more just very picky about "designed properly". For me, to be designed properly, the relay should be agnostic as to the bulb type, rather than relying on the resistance of the bulb to get a flash going. To me, the latter is cheap and lazy.

I think I'll get a couple of CF-12 relays like I have on the Rebel. They weren't terribly expensive and they do the job... I'll just have to relocate them is all.

But if I can find some round ones that are agnostic about bulbs, I'll get those instead since they'll fit... Maybe next month though. This month I'm kind of tapped on funds from doing the last bit of work to get the bike back on the road.

Round electronic LED flasher.

cwswiring.com --- creative wiring solutions --- LED flasher .... related KZR topic. pg 3. see flasher pic
cws main page -->> shop -->> LED / Incandescent lamp compatible flasher unit -->> product info & cross reference

There are multiple levels of "Heavy Duty" flashers... but heaviness of duty is not the issue, really, when using LED's.

What you want is an electronic flasher. But there are a couple levels of those.

Some use a capacitor circuit to perform the timing, but even those rely on the load somewhat. This type is usually inside of a transparent round case with two terminals.

The ultimate is one that is run by a digital timer circuit. Then the load won't effect the timing at all. The Wagner model 7060 used to be the most common version of this type. The only problem is the fully electronic, aka digital, flasher requires adding a ground wire for it to function properly. Once you do that, it works with any type of load.

Here are some really old notes on flashers: