Inside the white slider there should be a thermistor and a white wire leading out the back your refrig. To the control board. Sliding plastic piece up (colder) or down (warmer) controls the temp of refrig. If the thermistor is gone or faulty then the board goes into continuous mode.
As far as jack goes try eBay or Craigslist. Any RV shop should have them.
Jim and DW
2001 T-2553 Sunline Solaris
2006 GMC Sierra Duramax 2500HD 4X4
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Reese Dual Cam Sway Control