The 1 kHz test clip signal comes from a front panel board with its own NEC microcontroller. Start checking the 5V power supply to that board first. I suspect you will see the same ripple. Check with another scope first so that you know for sure what’s root cause: the signal on tge test clip bad, or the scope ADC etc bad.
If that’s not it then check the 2.5 V reference ic on the main board. It’s an 8 pin SOIC, on the middle of the board, near the corner of the metal covered part. Is it ripple free? Unlikely, but you never know. There’s another SOIC-8 closer to the very large IC MM9595. That’s just a dual opamp. Check for ripple on its outputs.
The 2 Hz you see might be aliasing. The 1 kHz comes from a front panel crystal but the scope itself has its own crystal, 75.7575 MHz. See if the 2 Hz goes up or down a bit if you heat up either crystal.