If you wanted to spice it up you might run across some of the Spanish Naval and Air Forces in the Caribbean and Southern US. Considering that their Naval forces and Maritime Patrol aircraft (P-3s and maybe their AV-8s) would have been running to support convoys between the US and Europe. So a Spanish ship stuck in a place like Puerto Rico, Grenada, some port in FL or the US Gulf Coast because of lack of parts, supplies, damage whatever might be a possibility. If not some left over planes somewhere that escaped nuclear attacks against the Spanish territories in the Atlantic (like the Canary and the prime NATO base at the Azores).
I would also wonder if the French might not have pushed into the Pyrenees in the T2K world to chase their own Basque and related terror groups. Let alone the historical "ownership" of territories in the Pyrenees near the Bay of Biscay that are real world Spanish land, used to be in the 1700s belong to the French.
Having been thru Spain more than a few times on my experiences with the US Military. The internal politics of Spain are very, very complicated to a US citizen. There is still plenty of bad blood about the Spanish Civil War (see the recent real world news articles about whether to dig up Franco and the rest of his lot and bury them in some unmarked grave or if that is dishonorable, it is almost to the same scale as the US Civil War debates). As well the Spanish had numerous terror groups that, if memory serves me right, that were being influenced or leaned heavily towards the KGB ruble for payment and advisory. So its Army more than likely would have been trying to lock down security and backing up its
Guardia Civil. Who are some folks, that I have seen operate in real life and they are the law in Spain. The Guardia aren't folks you mess around with, they like to use the baton first and ask questions after their arms get tired.
With respect to targets for nuclear attacks. Assuming that the Cold War doesn't end. Not only is Rota/Gibraltar a nuclear target. the USAF 16th AF has its HQ located at
Torrejon AB its roughly 30km from city center of Madrid. As well
Zaragoza AB that is up near the French-Spanish Border region. You could leave both of those bases alone if you accept V1 of the timeline where Spain with the collapse of NATO (see Italy pull out and Greece pull out, with the Germans starting the war) declares itself neutral and kicks out NATO forces from Spain. If you go the V2 route, then either have any potential nukes for these bases miss or they aren't targeted at all because the 16th AF will have moved all its forces out just prior to the use of nukes in 1997.
With respect to land forces OrBATs another idea is at Wargame Vault. There is a company there called MicroMark Army. They produced a number of PDFs for the Cold War armies.
Here is just the European selections and they do have listed both Spain and Portugal.
If you are curious as to what one of the lists looks like see the attachment of one I bought for another project. It is what a Canadian armored division looked like on paper when in Italy in 1943.