if it is a newer revision joystick control and it has the small LED window built in then yes there will also be a red dot on in it and also some LED bars showing the battery charge level. If it is an older revision joystick without the LED window then that red light is a fault indicator and the battery level indicator is several green lights usually across the bottom, at full charge all of them will light up and as it discharges they will fall off one at a time till the batteries need to be charged again. I believe the last light turns red and will not let the lift go up but it will still drive so you can get it to the charger. This is not the fault light, that light usually has an indicator with an exclamation point inside a triangle. (if your facia decal is damaged or worn off then of course you may not know which is which).
Can you tell me what the serial number of the lift is?
And as far as pictures forkliftaction does restrict hyperlinks without permission but you can use my email and send a couple to me if you like, it's in my post signature.