This sounds like EIA-608 subtitles (Wikipedia). They’re unique to the US, Canada & Mexico (who use the NTSC broadcast standard)…
They’re part of the video stream, not a separate track like PGS, SRT, etc.
Support varies across Plex clients. I don’t have an ATV with which to test. Enabling them in Plex for Android/Android TV and Plex Web results in a video transcode. They direct play when using Plex for Windows.
I’ve never tried it, but here’s a thread about converting them to SRT format:
Here’s the output from MediaInfo for a file with EIA-608 subtitles.
Summary
General
ID : 1 (0x1)
Complete name : Have Gun -- Will Travel (1957) - S01E01 - Three Bells to Perdido.ts
Format : MPEG-TS
File size : 228 MiB
Duration : 29 min 58 s
Overall bit rate mode : Variable
Overall bit rate : 1 065 kb/s
Maximum Overall bit rate : 35.5 Mb/s
Video
ID : 4113 (0x1011)
Menu ID : 1 (0x1)
Format : AVC
Format/Info : Advanced Video Codec
Format profile : High@L3.1
Format settings : CABAC / 4 Ref Frames
Format settings, CABAC : Yes
Format settings, Reference frames : 4 frames
Codec ID : 27
Duration : 29 min 58 s
Bit rate mode : Variable
Maximum bit rate : 40.0 Mb/s
Width : 854 pixels
Height : 480 pixels
Display aspect ratio : 16:9
Frame rate : 30.000 FPS
Color space : YUV
Chroma subsampling : 4:2:0
Bit depth : 8 bits
Scan type : Progressive
Audio
ID : 4352 (0x1100)
Menu ID : 1 (0x1)
Format : AAC LC
Format/Info : Advanced Audio Codec Low Complexity
Format version : Version 2
Muxing mode : ADTS
Codec ID : 15-2
Duration : 29 min 58 s
Bit rate mode : Variable
Channel(s) : 2 channels
Channel layout : L R
Sampling rate : 48.0 kHz
Frame rate : 46.875 FPS (1024 SPF)
Compression mode : Lossy
Language : English
Text #1
ID : 4113 (0x1011)-CC1
Menu ID : 1 (0x1)
Format : EIA-608
Muxing mode : SCTE 128 / DTVCC Transport
Muxing mode, more info : Muxed in Video #1
Duration : 29 min 58 s
Bit rate mode : Constant
Stream size : 0.00 Byte (0%)
CaptionServiceName : CC1
Text #2
ID : 4113 (0x1011)-1
Menu ID : 1 (0x1)
Format : EIA-708
Muxing mode : SCTE 128 / DTVCC Transport
Muxing mode, more info : Muxed in Video #1
Duration : 29 min 58 s
Bit rate mode : Constant
Stream size : 0.00 Byte (0%)
Report created by : MediaInfoLib - v21.03
Report created on : UTC 2021-09-06 01:02:18
