Hello, what I did with my dashcam was run the cable to the glovebox as you have, but I haven’t cut the cigarette lighter plug off and it just plugs into the cigarette lighter in the glove box absolutely no problem. No cutting of any wire or warranty issues etc. Mine is also the Nextbase dash cam
Good plan. Drilled 11mm hole top rear of glove box and cable went through all be it a tight squeeze. Camera now fully working and no cables on show or risk to warranty !.,