A quick look at GSV shows that (in 2024 at least) there was a sign at the entrance saying that Glasgow Airport Byelaws applied in that area. You would be well advised to look them up and see what they say about parking.
As stated, you probably also want to do the following:
1. Go back and get pictures of current signage.
2. Appeal as keeper. Don't name the driver. There's no keeper liability in Scotland so they can't transfer it to the keeper.
3. If you weren't the driver, say so. If you were the driver, don't lie. Just keep quiet.
However, the value of the claim puts you in a pickle. Parking companies don't normally do court in Scotland because the value of the claim is such that they can't recover expenses so hiring a lawyer is a waste of money. For a claim of £1400, they could claim expenses of up to £150 if they win, which might make them feel it's worth a shot.
If they send a lawyer to court they'll have an opportunity to ask you (the keeper) who was driving. I don't need to tell you how bad an idea lying in court is.
They know your identity as keeper. If you have any social media photos showing you on holiday for the 2 weeks you were parked next to the airport now would be a great time to make sure they're private.
If the worst comes to the worst and they do take this to court, you may also have a partial escape route. They've said that the contravention is no parking at any time. The vehicle was parked once, so one ticket is potentially valid. If they'd issued one ticket for £1400 saying it's £100 per day then fine, but they haven't. they've issued 14 tickets, which implies 14 separate contraventions. But if the driver was in Benidorm for the entire day the car was there and never touched it, they can't have formed another contract. This avenue will likely depend on the signage and / or the byelaws.