Topic: Powering a DPA 4060 with a battery inside an acoustic guitar?

[Uncoupled]

I have a custom acoustic guitar with a DPA 4060 mic wired to the ring of a TRS stereo output jack (tip is wired to a transducer pickup). The guitar has another output jack that's wired to a magnetic pickup powered by a 9V battery affixed inside the body of the guitar. This jack has power switching for the battery. The DPA takes 5-10V bias voltage and this is normally supplied by a multi-channel instrument pre on the ring.

Now, is it possible to use the same 9V battery that's currently inside the guitar to power both the magnetic pickup and the DPA 4060? If so, can the TRS output jack connected to the DPA+transducer do the power switching for the same battery as well (I believe the jack is from K&K and has that 'feature'). No big deal if not, as I can always have a second jack connected.

If they both can't share the same battery, can the DPA be powered by a different 9V battery inside? If so, how would I go about getting this?

The DPA 4060 is currently wired straight to ring of the TRS. No microdot adapters or converters used anywhere as far as I can tell, and my preference would also be to not have them inside or outside the guitar to minimise the number of parts.