Like most skinheads in America, I was heavily into the rockabilly scene for about 10 years after "retiring" from the skin scene in the mid 90s....

If there is any ivy influence in Rockabilly/vintage 50s style, it's minimal and definitely not deliberate.  If anything, most purist rockabilly guys would have considered Ivy style to be "not rockin' " and shunned it.

Shirts are almost always rayon gabardine, rarely buttondown and preferably adorned with atomic prints.

The closest "ivy" style garments I can think of that might have crossed boundaries are varsity jackets and of course selvedge jeans.  Before the big mainstream selvedge jean kick that every internet forum kid jumped on in the past 3 years, rockabilly cats have been wearing for years when no one else knew what selvedge was (other than japanese denim purists).  Back in the 90s one of my rockabilly friends from Tokyo paid almost $10,000 USD for a pair of vintage 1937 501xx bucklebacks if you can believe that!!

and it's always weird how Morrissey gets mentioned when it comes to skinheads and rockabilly.  The skinhead connection I'm guessing is from his fairly nationalistic stance on Britain, posing draped in the Jack, having been a later era singer for Slaughter and the Dogs (!!), and as a solo artist one of his biggest hits is called "Suedehead" even tho the lyrics have nothing to do with the cult.   His Rockabilly connection is probably more to do with his hairstyle, being a pompadour of sorts, and his solo band's guitar player is Boz Boorer from the Polecats who were a huge neo-rockabilly phenom in the 80s

It's only recently I've started to realise that loads of the clothes I was wearing as a young rockabilly/psychobilly totally fitted into the whole Ivy aesthetic. Madras shirts (white T showing underneath) baseball jackets (I had a particularly fetching black and silver LA Raiders number) varsity sweatshirts, chinos, baseball boots etc. Mostly all bought from Flip of course. It was rockabilly, and bands such as The Vibes and The Cramps that led me toward the Garage Punk sounds of The Sonics et al and eventually back round to British R&B and the mod scene leading me more towards a more mod influenced look and latterly a more Ivy look!

It's interesting how all these tribes relate to one another, I'd say the common link is ATTITUDE.  Whether it's skins, mods or rockabillies there is always (at least for the dedicated) an attention to detail and an effort to look sharp/tidy, albeit in his tribe's "colors".

When I first started going to rockabilly shows in Fred Perry shirts it was funny how many guys came out of the woodwork to talk about how "they used to be skins too"....but it seemed everyone sort of took their cues at the same time.  A lot of skin friends who I hadnt talked to in years I found out got into rockabilly at the same time as me, and then we all went back to our roots at the same time many years later.  It's like we were all functioning telepathically or something.