You have a 4bta and a T19 on a S10 chassis and you are wanting an "original" foot start? Wow! That's odd as hell.
I suppose you would just turn on the glow plugs with an ignition switch on dash and rig a sealed, momentary, normally open, push button, switch. To be operated by a "looks like original" foot peg on the floor. Said switch would operate the solenoid. Simple.
Unless there is something different about a diesel. I know nothing about diesel starting system.
Also what is this "lever switch" everyone is talking about??? the old foot stomp, linkage operated switch on top of the old starter?
There would be no need for a relay. The solenoid is a relay.
Would like to know how much of the original foot start mechanism you have so I can suggest a modification. A pic or two of hole in floorboard and clearance around that hole in engine bay.