Possibly me who fitted a manual fan switch, Kit?
I fitted it as an overide, so the stock fan switch will (should!) still operate if the coolant reaches the set temperature. My bike's a Legend TT (885 T3 motor, lower tuned) - or started out as one anyway

. I fitted Trophy/Trident clocks a while back after the original Tacho had it's own ideas about engine revs, & hooked up the temp gauge as well. I noticed then that in all riding conditions/speeds except really slow stop/go conditions the temperature stayed nice & low, beteen 1/4 & 1/3 up the gauge. But in city stop/go situations, the temp rises rapidly, 3/4 or a tad more up the gauge, & the engine clearly didn't like it. It also tended to spit out some coolant too. Likely the oil temp is going up quite a bit too. Not great.
IMO the fan switch temp is set too high & by the time the fan does come on, the fan struggles to bring the temp back down. After the head gasket let go on my buddy's Tbird Sport last year, I heard a number of comments, incl. one from Sandy at Triumphant who specialises in rebuilding T3s (among lots of other Triumph goodness), that head gaskets/head warping can be a weak area on these engines - not big nos of failures, but some. Seems to me that elevated temps, perhaps a little coolant loss that goes unnoticed, could well be a contributory factor. The switching set point of the fan switch could 'drift' as well, how would we notice? Overall, the issue may be minor in how often it becomes a serious problem, but for me, I see it as cheap insurance.
When the temp is spotted rising a little & I may be stuck in traffic a while , I switch the fan on & it has no difficulty in keeping the temp normal. Handy for a carb balance/tuning session too, to maintain engine temp around normal.
It sounds like a PO did this mod on your (OP's) Trident? If they did, it's most likely that they just paralleled onto the existing fan switch connections. No reason not to, & it's a convenient point to wire into. Shouldn't be too hard to follow the wiring back & see. They possibly used a relay, as I did, with the switch/relay coil + feed taken from an 'ignition +' line. That way the relay drops out when the ignition is switched off.
If the mod looks like this & done properly, I'd keep it

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