According to the 1958 Chevrolet truck shop manual: The 6 used a foot switch and the 8 used a key switch. It shows a wiring diagram for each one with different ignition switches. It does not show a starter button under the dash. The 1959 suppliment manual shows no changes to the wiring diagrams, thus making this effective for '59 also.
I have a '59 with a 6. I ordered a new ignition switch from Chevy Duty and they sent the one for the V-8. I called them to explain and they claimed there was only one switch and if mine wasn't like theirs someone had put the wrong one in mine. I told them to look at the wiring diagram in the shop manual they also sell and they insisted they were right and no need to look it up. So I asked for a return authorization which I got no problem. My switch was good but I didn't have a key. I ended up drilling out the old key cylinder and installing a new one. It works like it should.

"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.