Ordinarily, with the F250 camera, the only way you could get the tally lights to come on, is when you have the camera connected to a CCU. Without it connected, the camera's operating mode changes, and it ignores the tally input pin on the 32-pin connector. Certain portions of the interface circuitry in the camera adaptor, between the multipin connector and the camera head is disabled. Quite why they do that, I do not know, I do not see the value in disabling the function.
If you're never going to get a CCU, then a simple modification allows you to bypass the camera's interface, and provide your own. The circuit for this is provided, below. If you might obtain a CCU, you'll want to modify it in a different way, so both methods still work. I'll leave that problem up to you to solve. This modification will allow you to trigger the tally lights on the viewfinder, but the one on the back of the camera adaptor will not work, because it's connected to a switched power supply, and that power supply is switched off when there isn't a CCU connected to the camera.
Locate connector 12, a 12-pin connector, that connects the 32-pin camera connector to the mother board in the camera adaptor back-end. Interrupt the wiring to pin 7, insulate the end going to the motherboard, and take the end leading to pin 5 of the 32-pin camera connector. It may be possible to simply splice into that line, leaving it going to the original circuit, and your new one, but I haven't tried it (in this case, you simply join your interface to the connector's pins on the back of the circuit board, rather than cut into the wiring). This is the tally input to the camera, and you'll connect it to your interface.
Locate connector 4, on the main board in the camera adapator back end (the one with all the components on it). Its pin 1 is the tally signal to the camera head, and you're going to connect your interface output to this pin (directly to the pin on the back of the board, without changing any of the original wiring to that pin).
Locate connector 7 on the same main board. It's pin 2 is a +8.8 volt supply that you're going to use to power your interface. You'll connect to the pin on the back of the board, without changing any of the original wiring to that pin.
Locate the ground test pin on the same main board. You'll use it, or a point near it, to ground your interface circuitry.
Your interface circuit consists of two 10kΩ resistors, one signal diode (such as a 1N914), and one PNP transistor (such as a BC559). Connect the two resistors in series between the +8.8 volt supply and the transistor base. Connect the diode between the tally input pin and middle of those two resistors, with the cathode facing the tally input on the 32-pin connector. Connect the transistor collector to the ground pin. Connect the transistor emitter to the tally pin on connector 4, leading to the camera head. And that's it. The circuit is so basic that you could simply fit the components inside heat shrink tubing, wired point to point, without using a circuit board, and stow it into the cavity of the camera adaptor back end.
Your new tally interface is an active-low, or ground-closure, input. When you ground the tally input, the tally light will come on. This suits the tally output of most vision mixers. And your interface provides some protection to the camera circuitry, in case of accidents.
The diode on the input prevents false triggering of the tally when multiple tally inputs are tied together (e.g. mixer tally out to camera tally in, and to preview monitors tally inputs, and to audio mixer audio-follow-video switch inputs). Without diode-coupled inputs, each input drags the impedance further down towards to ground, until the all the tallies are switched on all the time, especially if one of them has a low impedance to ground, to begin with.