Pulse rate(definitely) and blood oxygen (I think) change drastically between delta and REM. Thus can be used to determine REM.
Like I said it has snags, like determining that change requires some logic, and thus some digital electronics
And it has to be adaptable to determine the high and low levels for each individual

On the positive side, it means with a little extra work, you could gather information about the vital statistics of a person while sleeping, and determine their REM cycles