At its peak we were running 2 X west Worthing to Seaford an hour and 1X Littlehampton to Eastbourne an hour and vice versa if I remember correctly. I know the coastway west to Eastbourne we’re 2Rxx train running codes.
Time to unearth some timetables! So, in summary, from the GBTTs I have:
10/1993 nothing shown cross-BTN
5/1994 1tph EBN-WWO Sats & M-F approx 0900-1500 only
9/1994 ditto but extended across M-F peaks
5/1995 to 9/1996 1tph EBN-WWO plus 1tph SEF-LIT. Odd jnys (early/peaks) to/from Bournemouth, Hastings, Lewes &c instead
6/1997 to 9/1998 as above but most off-peak Eastbournes to/from Seaford instead
9/2000 reduced to 1tph SEF-LIT off-peak & Sats, 2tph M-F across BTN M-F peaks, various origin & destination
5/2001 to 9/2002 1tph SEF-LIT, approx 1tph across BTN M-F peaks, various O&D (correcting my summary above)
5/2003 nothing shown cross-BTN
Caveats: there is no consistency across the 2 tables (188/189) as to what is shown running through (to/from) so WTTs needed for full picture.
Some of the evening shuttles HOV-BTN are shown as running through to SEF (mostly this direction only), otherwise by 1900-2000 the through service ceases.
In summary, it appears that the through service was a trial that started slowly under NSE, expanded gradually and was retained by Connex but abandoned by SouthCentral, lasting around 9 years in all, far longer than I remember. It would be interesting to know how much new traffic it actually generated, how reliable it was (given the operating constraints at Brighton) and how much disruption it caused to BML services.