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TIP120 is too big. Not saying it won't work... but it's like using a sledgehammer to push in a thumbtack. To pull a signal line low, you just need a small signal generic device, like a 2N2222. The FANs RPM sender usually have an "open collector" NPN device that PULLS the signal LOW when the RPM magnetic sensor engages.
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Seriously... my advice is to get the right fan and install that.
Any fan that "needs to warm up" is not one that I want keeping my parts cool. That's a sure way to eventually lose more than just the fan.