I think you don't actually have things connected as you've described, or you have the mosfet pinout wrong, or it's not the mosfet you identified. I don't know where to go from here. But let me ask again, what is the voltage on the three mosfet pins when D2 is high and the mosfet is supposed to be on (no diode)?
That is the test code we are using while we try and figure it out... It's just a easy on off on pin 2 for output. I'm sorry I can't offer you what you need asap as I said before I'm trying to help my 13 year old son. I have no understanding of Arduino stuff... Although I do have a ton of 12v DC knowledge from being an automotive electrical tech and accessories installer. But we never got into hooking up MOSFETs... Like I said before I appreciate anyone's input and apologize for the missing info, I'm trying my best to get all this while life is happening.
The original diagram with the lamp had the resistor as a pulldown to ground from the D2-to-gate connection, not inline between them as you apparently have it. The pulldown version is the correct one. It's there only to make sure the mosfet stays off when it's supposed to be off.
But we still have the situation where the gate-source voltage is 5V, but the mosfet is off. That shouldn't be possible. Can you double check the mosfet part number, and the pinout as shown in its datasheet?
BOJACK RFP30N06LE MOSFET 30 A 60 V RFP30N06LE N-Channel Power MOSFET Transistor ESD Rated TO-220 (Pack of 10 Pcs) https://a.co/d/bKdp6C9
Those are the MOSFETs we ordered, being that they are Amazon they could be wrong? Or bad, but we've tried all 10. Thank you for helping... I appreciate it!