I applied this patch but had some issues.
I used RGN Tool and changed the SW version from 850 to 851.
Saved the gupdate.gcd file in Garmin folder but nothing happened on the device.
I found a file with the same name in .System folder, renamed it and put my patched file in there.
Turned on the device and after a while it informed me that 8.50 (not 8.51) has been installed but the warning screen was still there.
1. Could you tell me what's the alternate method with pre boot mode? Should I change the software version on both methods and will be informed from Garmin WebUpdater when 8.51 comes out?
2. How could I restore the original firmware if something goes wrong from a modified firmware?
3. What settings did you use in IDA Pro? If I knew how to disassemble properly I could understand better what changes should be applied
Older Garmin devices update using gupdate.gcd in internal Garmin folder, new devices like your 2599 use the [hidden] .System folder. Renamed file  is still v8.50, the renaming is only to 'fool' the device into loading it via GCD. The modded V8.51 file can also be loaded by dragging it onto WebUpdater.exe or it's shortcut icon on your desktop, or using a Garmin root folder in microSD card [remove any existing GCD from .System first].
Using the fw file as an RGN via Updater.exe in preboot does not require a change in SW Version in RGN_Tool but you must ensure you use the fail-save naming convention: <hwid>01000<swv>.rgn and for your purpose that's 194701000850.rgn [again, remove any existing GCD first]. Any naming of RGN other than fail-safe '01000' will force the flash so be sure to check everything very carefully.
Clearly the patch hasn't worked if you're still getting the warning screen. You can restore original firmware by same methods using changed version GCD or by flashing in preboot with RGN.
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This will not eliminate the warning but will help finding the patch that will by verifying that sub_20754CFE is being called in the process of showing the warning screen. At file offset 0x6D4D94 patch from A7 6E CF AB to 26 C8 F3 2B. This should change the text of the warning to "Vehicles are not allowed on the road ahead. Take the closest exit to an alternative road."