Wiring a inverter generator back up pigtail to a Trane XE 90 furnace

[Falcon195]

Hello,
I am in the process of hooking up a inverter generator pig tail so I can use my generator for emergency power to my Trane XE 90 furnace
The issue I am having is I want to hook the 3 wire 15A pigtail to the Hot, Neutral and Ground to the furnace. But I don't have a ground wire coming from the board of the furnace. All I have coming from the furnace board is the Hot and the Neutral.
Now I do have a ground coming directly from the line conduit thought the outer switch box going directly to a ground connection on the inside of the furnace cabinet. BTW this ground wire from the line in through the outer switch box going directly to the ground connection on inside of the cabinet bypasses the on off switch on the outside of the furnace.
I am replacing the standard outer on off switch with a combination on off switch and a 15A outlet to plug the pigtail coming from the furnace board for normal usage. So when I have a power outage, I can unplug the the pigtail and run it directly to my inverter generator which has a floating ground and I will be using a neutral to ground plug in one of the outlets on my generator so I will be bonding the neutral on my generator. But I am confused on where and how to connect the ground wire coming from the pigtail beings I don't have a ground wire coming from board of the furnace.
Can someone give me some insight and this ground connection?
Thanks