edit: This was done with my wife's 2018 Model 3, although I imagine things will be pretty similar on a newer Model S. My 2013 Model S doesn't the hardware for the dashcam.
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Third time's the charm. First attempt used a five year old Centon 4GB stick formatted on a Windows 7 laptop. It saved one or two files and then gave the the gray x. A reformat made it work again briefly, but quickly got the gray x. Next attempt was a more recent Lexar 16 GB stick. I first formatted that on a new Windows 10 laptop. That one gave the gray X without even a single readable file. I then tried formatting the 16 GB stick on the windows 7 laptop. This time it mostly worked! It saved a mp4 file every minute. When you tap the dashcam icon, it changes the filenames from recent-front-XXXX to saved-front-XXXX so they don't get overwritten. The partial minute files when the car was turned off weren't readable on the Win 7 laptop.
Here is the text from the command prompt when I tried to read the files after the initial failed attempt with the 16 GB stick, reformatted the stick, and finally had some success:
D:\>dir
Volume in drive D is DASHCAM
Volume Serial Number is 72C4-876F
Directory of D:\
10/16/2018 07:00 AM <DIR> TeslaCam
10/16/2018 07:00 AM <DIR> .cache
The parameter is incorrect.
4,087,808 FSCK0000.REC
1 File(s) 4,087,808 bytes
2 Dir(s) 15,989,833,728 bytes free
D:\>cd TeslaCam
D:\TeslaCam>ls
'ls' is not recognized as an internal or external command,
operable program or batch file.
D:\TeslaCam>dir
Volume in drive D is DASHCAM
Volume Serial Number is 72C4-876F
Directory of D:\TeslaCam
10/15/2018 08:47 PM <DIR> .
10/15/2018 08:47 PM <DIR> ..
10/16/2018 07:07 AM 0 recent-front-2018-10-16_00-07.mp4
1 File(s) 0 bytes
2 Dir(s) 15,989,833,728 bytes free
D:\TeslaCam>format /FS:FAT32 D:
Insert new disk for drive D:
and press ENTER when ready...
The type of the file system is FAT32.
Verifying 15275M
Format cannot run because the volume is in use by another
process. Format may run if this volume is dismounted first.
ALL OPENED HANDLES TO THIS VOLUME WOULD THEN BE INVALID.
Would you like to force a dismount on this volume? (Y/N) Y
Volume dismounted. All opened handles to this volume are now invalid.
Initializing the File Allocation Table (FAT)...
Volume label (11 characters, ENTER for none)? DASHY
Format complete.
14.9 GB total disk space.
14.9 GB are available.
8,192 bytes in each allocation unit.
1,953,276 allocation units available on disk.
32 bits in each FAT entry.
Volume Serial Number is 10E9-19FF
D:\>mkdir TeslaCam
D:\>dir
Volume in drive D is DASHY
Volume Serial Number is 10E9-19FF
Directory of D:\
10/16/2018 06:08 PM <DIR> TeslaCam
0 File(s) 0 bytes
1 Dir(s) 16,001,228,800 bytes free
D:\>dir
Volume in drive D is DASHY
Volume Serial Number is 10E9-19FF
Directory of D:\
10/17/2018 01:33 AM <DIR> TeslaCam
10/17/2018 01:11 AM <DIR> .cache
0 File(s) 0 bytes
2 Dir(s) 15,387,844,608 bytes free
D:\>cd TeslaCam
D:\TeslaCam>dir
Volume in drive D is DASHY
Volume Serial Number is 10E9-19FF
Directory of D:\TeslaCam
10/16/2018 06:08 PM <DIR> .
10/16/2018 06:08 PM <DIR> ..
10/17/2018 01:12 AM 27,973,564 recent-front-2018-10-16_18-11.mp4
10/17/2018 01:13 AM 30,456,605 recent-front-2018-10-16_18-12.mp4
10/17/2018 01:14 AM 30,408,858 recent-front-2018-10-16_18-13.mp4
10/17/2018 01:15 AM 30,343,261 recent-front-2018-10-16_18-14.mp4
10/17/2018 01:16 AM 30,015,201 recent-front-2018-10-16_18-15.mp4
10/17/2018 01:17 AM 30,513,316 recent-front-2018-10-16_18-16.mp4
10/17/2018 01:18 AM 30,165,710 recent-front-2018-10-16_18-17.mp4
10/17/2018 01:19 AM 30,144,592 recent-front-2018-10-16_18-18.mp4
10/17/2018 01:20 AM 30,284,407 recent-front-2018-10-16_18-19.mp4
10/17/2018 01:21 AM 30,655,666 recent-front-2018-10-16_18-20.mp4
10/17/2018 01:21 AM 12,339,145 recent-front-2018-10-16_18-21.mp4
10/17/2018 01:26 AM 30,367,826 saved-front-2018-10-16_18-25.mp4
10/17/2018 01:27 AM 30,635,170 saved-front-2018-10-16_18-26.mp4
10/17/2018 01:28 AM 30,504,501 saved-front-2018-10-16_18-27.mp4
10/17/2018 01:29 AM 30,523,364 saved-front-2018-10-16_18-28.mp4
10/17/2018 01:30 AM 30,590,237 saved-front-2018-10-16_18-29.mp4
10/17/2018 01:31 AM 30,420,297 saved-front-2018-10-16_18-30.mp4
10/17/2018 01:32 AM 26,839,287 saved-front-2018-10-16_18-31.mp4
10/17/2018 01:33 AM 30,495,772 recent-front-2018-10-16_18-32.mp4
10/17/2018 01:25 AM 30,427,273 saved-front-2018-10-16_18-24.mp4
10/17/2018 01:33 AM 16,015,647 recent-front-2018-10-16_18-33.mp4
21 File(s) 600,119,699 bytes
2 Dir(s) 15,387,844,608 bytes free