I believe it wont come on with just the button.. It needs high pressure from the AC coolant. Which is no longer there.

Now I have never ran bothfans, never bothered. Been happy with the plastic oem fan. What ever model that comes on. But I do have my single fan controlled by the EGR solinoid out put. It turns the fan on, above 190° and dose not shut off unless Im at full throttle. That might be an easy short wire job for you.

11.45@125,
stock bottom end 6bolt 2g head.
272 hks cams.
Holset hx35
Backyard biult!!