How do I make a "Team only vehicle seat script"?

You need to check as soon as the occupant changed whether or not the given player is of a certain team. If he is not you can force jump him to get him out of the seat.

Example:

local seat = script.Parent -- Change this as needed

seat:GetPropertyChangedSignal("Occupant"):Connect(function()
    local occupant = seat.Occupant

    if occupant then
        local player = game.Players:GetPlayerFromCharacter(occupant.Parent)
        if player.Team ~= game.Teams.YourTeam then -- Change YourTeam
            occupant.Jump = true
        end
    end
end)