Normally things don't happen that fast when brewing, I brew both beer & wine and usually take a SG reading & and a visual check to gauge when to rack.
It's not that a precise science.
One way around getting over the possible rotation of the air lifted float type, would be to place the button magnet on the top of the float, and use the S4xx sensor on the lid cover.
You can get really small button mag.
You could use a small button magnet attached to the float, (what kind do you have)?
A Honeywell S4xx sensor would detect the movement.
One problem may be if there is significant evaporation of the air lock liquid.
Another issue there is if the float happens to rotate!
Have you seen this post on similar make/issues?
https://maker.pro/forums/threads/sunbeam-electric-blanket-no-heat.281560/
I see that you did, no info there that helps?
Here is a simple DWG, the M (motor) would represent one of the windings, the other stays connected the same way., always stop before reversing.
This is for a simple DC motor but the switch action is the same for one winding.
IF it is a PSC, Permanent Start Cap motor, all you need is a SPDT switch in order to reverse.
Measure both windings, if they are the same then it is PSC and I can post you a simple DWG.
What type of heating element is it? Rod immersion type?
It may have been more economical to obtain a immersion style with the thermostat pocket fitted.
Fitting a separate one afterwards can be costly.
If this is a non-positioning application but variable speed is reqd, , ex-treadmill DC motors may work, they are 2hp -3.5hp.
There are the MC2100 controllers also, one source is T.M.s that often come up locally, Free for Pickup (not working).
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Very similar in practice to bi-polar electrolytic capacitors used in AC motor starting, where a very large capacitance value is required in order to provide the initial starting current.