Yes..... It can be done, merc has made two types of sensors for this that I'm aware of.........A two wire(passive single element) #17 below, or a four wire(passive dual element) not shown but would be in-place of #17, sensor for analog gauges.
Some engines came with both cylinder heads pre-milled(see below for thermal switch) to accommodate both the warning switch #10 sensor(star side usually) and the analog gauge sensor #17 I mentioned above(port side usually).
Above: One wire "overheat" thermal switch, item #10 above. Closed(rant = closes switch to a FLAKY held in place w spring ground/the hole :facepalm

if temperature reaches 240F +/- 8 F
As a quick work around(i'd still install the analog gauge, see "rant" above) perhaps use a non-contact I.R. thermometer next time it overheats if the neighbor has one

Unless something is shorting out on the T.S.'s output, I'd guess it's overheating, airpax makes those T.S.'s for merc(or used too) and those folks make good stuff. They are fused glass hermetically sealed, they rarely fail internally. However, I went to a two wire T.S., (see rant again)
And yes, the overheat warning sensor is just a switch.
As far as the gauge itself, personally I'd try to matched my dash's existing gauges however that may be. Since Faria makes(a high percent of OEM's) mine, I just went to Faria dealer.