Switch – add a single pole switch to an existing thee way switch with same power source

multiway-switchswitch

Hello and apologies for this newbie question.

I have a three way switch that controls recessed lights in an extension through a wall, one three way switch inside (basement) one three way switch outside (extension).

Outside (in the extension) I have a two gang box where the power source comes in and provides the power to the common and then the travellers for the three way switch inside (diagram explains it best):
my current three way switch

What I'd like to do is to add a separate single pole switch together with the first three way in the attached diagram, that controls a separate set of recessed lights daisy chained with 2 wire Romex.

I've seen it done where the layout is three way switch to three way and then lights but this is slightly different.

For the life of me I can't figure out how to have my hot and neutral available to the single pole switch to control the second set of lights independently.

Again, sorry if this is too basic. Appreciate any help and guidance.

Edited:
Adding a bit of context:

Current three way switch installation

Best Answer

It is simple and straightforward in this case. From the switch on the left take the hot neutral and ground to the new switch location. Then feed the hot (black) to the switch.

Now take the black to the other side of the switch with the neutral and ground to the new light location.

Install the switch and the black at the light will be the switched hot from the new switch you added.

This is the only location you can add with the diagram you referenced. If the hot and neutral are at the light, not the switched position, it will take 12-3 or 14-3 wire to do it, but it can not be done from the switch on the right.