A neat idea but it would be easier to find a key switch with a start position.

If you want to do it your way you might cut the end off the lighter socket then build a bracket to mount the existing button behind the lighter hole.

"It's just a phase. He'll grow out of it." Mama, 1964

1956 Chevy 1/2-ton 3100
1953 Chevy 6100 "The Yard dog"
1954 GMC Suburban Now with a new proud owner.