A good way to know is to measure the diameter of the stem. If you're not sure how to measure this then take the bike down to your local bike shop.
The headset on my mid-80s timberline is one of GTs 1" wacky ratchet systems but by the 90s this might have been changed for a more standard unit. Whether or not it is a 1" or 1-1/8" you could look at the Tange cartridge examples for sale from Rose bikes that would suit perfectly (or buy what your LBS has).