Here is a suggestion. I am assuming that you can derive +24 Volt from the machine.
The +12 Volt can be derived from the +24 V with a resistor and Zener diode.
Circuit Description.
Initial state:- relays A & B are released, capacitor C1 is discharged thus the output of U1a is high so C2 is charged to 12 Volt and the outputs of U1b & U2a are low.
Relay A operates when the Pedal is pressed, it starts the Main machine and charges C1 rapidly to 12 Volt.
The output of U1a goes low and thus the output of U2a goes high which turns Q1 on operating relay B.
Relay B starts the Secondary machine.
C2 starts discharging via R3 so the output of U1b goes low after about 0.5 second and thus B releases.
Relay A releases when the pedal is released. C1 starts discharging via R1 & P1.
When the voltage across C1 decays to the lower threshold level of U1a, the output of U1a goes high which causes the output of U2a to go high thus turning on Q1 and operating B and also C2 starts to charge.
When the voltage across C2 reaches the upper threshold level of U1b, the output of U1b goes low. thus Q1 turns off and B releases.
Setting up the timing.
The 40106 Schmitt Trigger IC has a wide threshold spread, so it is not possible to calculate the precise value needed for C1.
Also, electrolytic capacitors have a +/- 10% tolerance, so a 10 uF cap can be anywhere between 9 uF and 11 uF.
Therefore, you need to experiment with the value of C1 to give the correct timing.
I suggest that you buy three 10 uF, one each of 6.8 uF, 3.3 uF, 2.2 uF and 1 uF.
Then you can (if necessary) connect these caps in parallel, eg. 6.8 uF in parallel with a 2.2 uF will give you NOMINALLY 9.0 uF.
So I suggest that you start with one of the 10 uF caps temporarily connected as C1, set the pot to its maximum resistance and then measure the time from when the pedal is released until relay B operates for the second time.
This time needs to be about 11 sec. so that the minimum time is about 1 sec (ie. when the pot is set to its minimum).
So try each 10 uF in turn, and if none of them give you about 11 sec. then:-
1. if the time is <11 sec. you will have to put one of the other caps in parallel with the 10 uF
2. if the time is >11s remove the 10 uF and replace it with the 6.8 in parallel with say the 2.2.
EDITED to correct errors.