Don't feel too bad about having to buy a 3-pin relay.
I bought 2 of the exact 2-pin type in your photo from a Chinese supplier (I bought 2 because they were so cheap and I thought to have a spare for the KLE and Yamaha, both of which use the 2-pin variety. I also liked the idea of the adjustable flash speed as I am currently converting every bulb I can on the KLE to LED.
Well the first one lasted a day and the second a day short of two weeks. An (at least) 30 year old spare flasher that I found in my "hope chest" is now doing duty on the KLE, it flashes a bit fast, but I'll live with it.