37's output was messy with the scope on my car at least. 64's output is much cleaner and i did try it without the relay, there isnt enough there to drive the tach. this tach definitely needs to go 12 or higher than open.
You can't do it with a mechanical relay, it'll wear out very quickly and stop working. They are not meant to be switched on and off continuously.
Use a transistor or a SSR.