Seeking Replacement Thermostat for Vintage 1970 Whirlpool Fridge

I'm in search of a replacement thermostat for my 1970 Whirlpool refrigerator. The specific part number I need is FSB #547581. Unfortunately, the on/off switch part of the thermostat has stopped functioning, and I'm aware that these parts are no longer manufactured. To confirm the issue, I bypassed the thermostat wiring, which successfully started the compressor and initiated cooling. After running it for about half an hour, everything seemed to be working fine. Now, I'm looking for either an original part or a compatible replacement thermostat that will fit and function correctly in my fridge. During my search, I've come across other numbers like 8201507 and 992414, but I'm not certain about their compatibility or validity. My refrigerator is quite basic, lacking modern features like automatic freezer defrost or an ice maker, which probably contributes to its longevity. I would greatly appreciate any assistance or guidance in finding a suitable replacement thermostat for my vintage appliance. Thanks in advance for any help provided.