Keybind script in a vehicle doesn't work. Help?

The UserInputService actually is only client side so you will have to use a localscript to get the user input. You can send this information from the client to the server with remotefunctions or remoteevents, and then go from there.

Here's something I threw together as kind of an example of how you could send the input across:

Local Script in StarterPlayerScripts

local UIS = game:GetService("UserInputService")
local seat = game.Workspace:WaitForChild("Seat")
local event = seat.RemoteEvent
local players = game:GetService("Players")
local keycode = Enum.KeyCode
local keys = {keycode.F, keycode.N, keycode.R}

--Send info when input begins
UIS.InputBegan:connect(function(input, processed)--Get input
    if seat.Occupant == players.LocalPlayer.Character.Humanoid then --check if the input should be sent
        if input.UserInputType == Enum.UserInputType.Keyboard then --check if the input is the right type
            for i,v in ipairs(keys) do --find out if the input is one of the right keys
                if input.KeyCode == v then
                    event:FireServer(input.KeyCode, "began") --trigger the event for the server
                end
            end
        end
    end
end)
--Send info when input ends
UIS.InputEnded:connect(function(input, processed)
    if seat.Occupant == players.LocalPlayer.Character.Humanoid then
        if input.UserInputType == Enum.UserInputType.Keyboard then
            for i,v in ipairs(keys) do
                if input.KeyCode == v then
                    event:FireServer(input.KeyCode, "ended")
                end
            end
        end
    end
end)

Script inside the seat

local event = script.Parent.RemoteEvent
local forward = false
local reverse = false
local neutral = false
function handleinput(player, input, inputtype: string)
    print(player.Name.." "..inputtype.." "..tostring(input))
    if input = Enum.KeyCode.F then
        if inputtype = "began" then
            forward = true
        else
            forward = false
        end
    elseif input = Enum.KeyCode.R then
        if inputtype = "began" then
            reverse = true
        else
            reverse = false
        end
    else
        if inputtype = "began" then
            neutral = true
        else
            neutral = false
        end
    end
end

event.OnServerEvent:Connect(handleinput)

From these I bet you could figure out a way to make it work with what you had going, hopefully this will help!

Edit: I edited the script portion to show you how you could setup your bool values. I haven't run this myself and typed it directly in here so hopefully I didn't mistype anything.

Ok I tried this as a normal script and as a local script, both of them didn't work.

local event = script.Parent.RemoteEvent
local forward = false
local reverse = false
local neutral = false
function handleinput(player, input, inputtype: string)
    print(player.Name.." "..inputtype.." "..tostring(input))
    if input == Enum.KeyCode.R then
        if inputtype == "began" then
            forward = true
        else
            forward = false
        end
    elseif input == Enum.KeyCode.V then
        if inputtype == "began" then
            reverse = true
        else
            reverse = false
        end
    elseif input == Enum.KeyCode.F then
        if inputtype == "began" then
            neutral = true
        else
            neutral = false
        end
    end
end

event.OnServerEvent:Connect(handleinput)

local F = script.Parent.Forward
local N = script.Parent.Neutral
local R = script.Parent.Reverse

if forward == true then
    F.Value = true
elseif forward == false then
    F.Value = false
end

if neutral == true then
    N.Value = true
elseif forward == false then
    N.Value = false
end

if reverse == true then
    R.Value = true
elseif forward == false then
    R.Value = false
end