How could I make this integrated dust collection wiring work?

https://preview.redd.it/iixj7vrpd1od1.png?width=1280&format=png&auto=webp&s=5e89a7c2b62091b7b564fc57633d43385c9e2877

I am trying to set up an integrated dust collection system in my new workbench. I would like for the shop vac to turn on when the Router (item 3) or the track saw (item 4) is turned on and then turn off when either of those are turned off.

As it shows, Item 1 is connected to the wall outlet via an extension cord. Item 2 is plugged into Item 1. Items 5 & 6 will be plugged into Item 2. Item 3 is plugged into item 6. Item 4 is a cordless saw. And Item 7 is plugged into item 6 as well.

Item 6 is a vac switch that should turn on the shop vac when either the router or the track saw (in theory) is turned on and will turn the vac off after a delay.

I do not know how I would control the shop vac when I am trying to use the cordless track saw. I am comfortable flipping a switch to turn on and off the shop vac but I am not electronically savvy and I am not entirely sure how that would look or how to install/wire.

If anyone has any plans or ideas on how to accomplish this it would be greatly appreciated! Thank you!