There is no stereo output per se, on the guitar.
The 'stereo' jack has the Piezo signal on one side and the magnetic pickup signal on the other side.
If you use a stereo (TRS) cable in that (piezo) jack, you need the other end of the TRS cable plugged into a splitter box, or have a cable that goes from stereo on one side to two mono 1/4" plugs on the other side. (One mono plug will be the Piezo signal, and the other will be the magnetic signal.)
In this scenario, you don't need to use the guitar's 1/4" jack for the magnetic pickups at all... just the piezo jack.
The other option is to use two separate mono cables, one in each of the guitars jacks, and one will be piezo and the other magnetic pickup.