12 Volt Lithium Battery Individual Cell Regulator

if you held the button down instead of 'tapping' it

i'm sure you could over amp things

but thats NOT the right technique

but you could always use a 555 timer and a transistor or mosfet to fire the solenoid

or even use a bank of mosfets in parallel instead of the solenoid
press a button let the timer fire the circuit
get exactly the same 'weld time' every time