With these motors you really don't need the 'start button and stop button' control box (DOL)- the simple old fashioned 'latching single emergency switch/ on/off' ones work perfectly well (and are a lot more reliable)
These usually have an arrow on them, like this...
Look for 'latching' rather than 'momentary contact' or NC/normally closed- to start the motor, pull it out and twist in the direction of the arrow, to stop- just hit it...
No contactors or relays, just a simple mechanical switch (they don't work on motors with a 'dual capacitor' arrangement ie a start capacitor and a run capacitor' but yours appears to be the simple old fashioned single cap 'run capacitor' only variety as are most motors)- you can considerably reduce the amount of cludged up wiring in there- fit a new power cord- (looking closer, that suspected VIR is the main power cable in!!!) and a general tidy up is definitely advisable...
Yours (some clearer pics would be a good idea to confirm it, but pic 6 seems pretty clear it is the 3 wire version- the earth wire doesn't count here lol) appears to be the three wire version top right...
compare to pic 6
In which case it would be wired like this with your colours
(the black joiner in my diagram up the top is the existing black 'BP' screw connector hanging out on the right in the 'control box in your original pic 4- which goes on down to what I suspect is likely a very dried out capacitor sitting on the wood block at the bottom...)
I would get some Wago connectors (originals, not the cheap Amazon/Ebay knockoffs)- fit a new powercord (if it is indeed VIR as I suspect- it is likely in VERY poor shape and extremely dangerous and could short internally if bent or flexed!!!) and disconnecting one wire at a time- replace that old BP connector with a Wago, then wire it with the new switch according to the diagram (them using all brown wires doesn't help grrr)
If you can get a clear shot of the markings on that suspected capacitor, a replacement for that is advisable as well (if it has dried out and changed in value, it could cause the motor to run hot, have reduced power and possibly damage it even!!!)
This thing...
It likely has a number (probably somewhere between 50 and 150 with MFD after it- that is the old fashioned marking for microfarads or uF- get a modern replacement rated at 400v or higher with the same number in uF
This is one I was working on earlier for a mate interstate lol
His original (80uF marked as 80MFD)
and the replacement...
He had been searching for hours for a 80MFD one, and couldn't find one- not knowing that that was just the old way of writing 80uF's lol- he had been looking at literally hundreds of suitable replacements and ignoring them because they didn't say MFD...
(he's a nurse, not an electrician lol- I go to him for medical advice, he comes to me for the 'sparky stuff' lol)