On a DX1000/DX2000 series with the remote suffix code /R1, can I start/stop recording using an external voltage level signal?

Yes.

• Settings
  1. Set the input terminal mode to "DI," the range to "Level," the upper-limit alarm to "1," and the alarm output destination to "Internal switch."
  2. Set the relevant internal switch as an event trigger of an event action and set the execution action to "Memory."