Yes, almost certainly a failed rad thermal switch.

Interesting, I haven't seen a rad without the thermostat mounted in a rubber press-fit collar on the rear at the top right corner, but there are obviously variants out there from other manufacturers sized to fit the rad mounting and trans cooler lines. Doesn't really matter where the thermostat mounts as long as the wires reach (or are extended). Those switch mountings you show would actually be a slight improvement in design as the stock switches are known to blow out under excess pressure (actually had that happen once).

I wouldn't want to force the mounting collars on an aging plastic tank if they don't come off with only moderate force after using something like PB-blaster. Restraining the spade connectors as a counterhold would certainly help, doesn't matter now if they get damaged or break off. Unlike the trans cooler lines, which are solidly attached on the inside to the metal core structure and can take quite a bit of force, I rather suspect there is just a smallish metal (or nylon) flange as reinforcement inside the side tank to support the types of switch mountings you show.

One DIY thought I had as a hack for your friend to avoid buying an expensive new rad is to leave the old thermostat in place and instead use an external thermal switch surface mounted on the rad side tank. These can be had for as little as a couple of dollars on places like Amazon. You would need a normally open thermal button switch (thermostat) that has a suitable temperature, rated for at least 12 volts DC (many are rated for 240 volts AC) and can handle perhaps one amp (many can handle well over 10 amps). Being surface mounted it wouldn't be as sensitive to actual coolant temperature as the stock thermal switches which has direct contact. Something that kicks in not too far above maximum ambient air temp, say 50-60 deg C, would detect when the coolant thermostat is open and the fan might be needed. Initially it could be surface mounted on a flattish area of the side tank using a zip tie between the spade terminals wrapped around the side tank through the core (as many recommend for the stock sensor). Once you're satisfied that it's working you could later expoxy it in place to protect it from the elements (JB-Weld, add a zip tie for good measure)) with perhaps a little electronic thermal paste (used with power transistors and CPUs) between the button surface and the side tank to improve thermal conductivity. See my other reply in this thread to Bob Ritter suggesting that operation of the thermal switch may not be all that critical.

https://www.jaycar.us/normally-open-thermostat-switch-50-degrees/p/ST3831

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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now