It's basically an electrical fuel cut-off.
The idea is that when you switch the ignition off, it prevents run-on by closing the valve inside and so stopping fuel going through the idle jet.
As to soldering on a new connection... well I've done it in the past with no probs, so unless you're a complete clutz with the soldering iron should be all good !!!
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'70 Hillclimb Bug 'Jezebel' w/- Haltech EFI -
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'60 KG Coupe - resto kinda started
01 New Beetle - gf's car, but I turn the spanners