Double checking 220v to 110v conversion

[SirWarrior]

I have 110v outlet in the garage I need to run my air compressor from. Due to outside factors, I cannot run 220v in the garage.
My solution is to switch my compressor to run 110v and I'd just like to double check if I read the schematics right.

these are the lines that are in the current setup -apparently previous owner didn't think Ground wire was needed

The wiring shows that I need to tie T2 to the T4 and T5 that the brown wire is going to currently and tie P2 with T8 and T3.

Obviously I'm going to get some new 3 core wire and use a 110v grounded socket.

I am fairly confident I got the above correct, but Im not 100% sure about the following:
P1 should be left by itself going to smaller prong while T2,T5,T4 bunch will got to the fatter prong and ground going to the green screw on the housing.

Can someone confirm my findings

 

[Greatbear]

It's difficult for me to see the low voltage wiring diagram but by your description and my experience, you have the right idea. The "Ungrd Line" in the diagram is the black wire, "line" is the white (or brown in the case of your wires). Get some fresh cable (1ga. minimum, 14ga. preferably) and use that. Grounding all the components (the motor and pressure switch in your case) is best. Use the green screw as you said.