Hi Bill, As so oft a short question - and a long answer!
A) Your Caldercraft ESC;-
It's deffo of older vintage, ca 70s-80s, and obviously still uses a relay for reversing.
And most probably Darlington pair transistors for the power control.
Low resistance FETs (Field Effect Transistors 😁) started to appear in RC equipment at the end of the 80s.
I don't know how you tried to 'breath life' into your ESC, sounds uncomfortable😮, but I would proceed as follows;
I see it has an 'arming' switch, unusual back then suggesting that it might be one of the earliest with a BEC, so-
* connect to a 6 or 12V battery, no motor or RX at this stage,
* check with a multimeter if there is any voltage (~ 6 or 12V) between the black and white wires on the switch.
If the switch is ON there will be 0V, if the switch is OFF there should be 6 or 12V less maybe 0.5 to 0.7V.
I would guess that the LED should also light when the switch is on.
Also; if the ESC has a BEC cct (which the 'arming' switch suggests) then when the switch is ON you should measure 5 or 6V between the black and red wires of the RX cable.
If neither of the above is true the switch maybe faulty (I hate these little slide switches, I prefer to swap 'em for a decent positive acting toggle switch).
Test by shorting out with a small pair of pliers or a chunka wire.
If the above is true, i.e. the switch has volts on it, connect the ESC to a Servo Tester in lieu of TX and RX.
Set the three trim pots of the ESC to the middle.
Connect a test motor and battery,
Ensure that the switch is ON, check with an Ohmmeter / continuity tester on your multimeter,
Twiddle the servo tester slowly from one end to the other and check a) the motor runs forwards and backwards, b) the relay clicks when you go from ahead to astern or vice versa.
If result a) is zilch then I'm afraid you've gotta dead ESC. RIP ☹️
Either a dead control chip (basically the same as in servos in those days) or blown Darlingtons due to excess current drawn, stalled prop for instance.
If the motor runs with controllable speed forward but not back, no 'click' from the relay, i.e. stops when it should be 'in reverse' or continues to run forward, then either the relay is kaputt (burned out coil) or the relay driver transistor.
The ultimate test (which I do) is to look at the ESC output with an oscilloscope, to check that it outputs a variable DC pulse train according to the servo tester (or TX/RX) control setting.
However I do appreciate that not all model boaters have a scope available 🤔
If the motor turns at all then set the servo tester to Neutral, full ahead and full astern in that order and adjust the ESC trim pots to suit.
If none of the above helps do you want to send it to me to have a closer look at it?
B) Your GWS RX:
I agree with Geoff.
The RX should work with any 35Meg FM (narrow band) TX.
You just need a corresponding pair of crystals. Make sure that they are FM and not AM crystals!! AM crystals MIGHT work but compared to FM crystals they will be unstable in an FM set and the usable range may be considerably reduced.
Happy testing. 🤞
If nowt works send it to me, I enjoy a challenge 😁
Cheers, Doug 😎
EDIT: Ps I note in pic 3 that the red lead from the RX is visible across the 'Speed' trim pot which has been displaced! This indicates that the ESC has been opened - suggesting that it has already malfunctioned and been opened! So you may have inherited a fault 🤔
NEARLY FORGOT😮: You may need to 'teach' the ESC where Neutral (All Stop) and where Full Ahead are, by appropriate movement of the throttle stick (and trim controls) and watching for the LED blink to confirm each setting.