He could be having a reaction to what the vaccination is suspended in
That is a good possibility. A lady on another forum works in the equine bio-tech world and has said for years the adjuvant in vaccines is generally the trouble-maker
I have one horse, of four, that has always been drug sensitive.
Fortunately I don't show and the short time he was boarded, it was a very small private barn way out in the country. Meaning I didn't have to pump him full of every vaccine known to mankind.
He is so drug sensitive, he can't have bute - half tablet will drop him to his knees.
When power tools were used on his teeth, the amount of sedation he required wouldn't phase the whiskers on a Quarter Horse. He's a Tennessee Walker and they are on the drug sensitive side.
These days all my horses get is a rabies shot. The vet gave him his rabies shot in the butt, to help reduce the reaction, and he stayed an extra 30 minutes to be sure Duke wouldn't drop to the floor and not get up.
Duke did have a mild reaction but he snapped out of it.
Duke is now 25+ and gets worse as he gets older - so that is something else to be considered.
I don't have an answer as to how approach the vaccinations but wanted you to know, there are other horses with drug sensitivities and it is possible the sensitivity might increase as the horse ages.