What impact would a TSSA strike have on the railway anyway.
Most footplate staff are ASLEF, the "man* at the back" and signallers are RMT.
Management would presumably step into supervisory roles.
Back office work would be affected and booking offices. What else?
* including women at the back
What impact would it have? Well, immediate concerns could include...
There would be no control staff,
No conductor or driver managers (including those with on-call and TOLO etc responsibilities),
No finance staff to run the payroll,
No rolling stock management on-call to authorise trains running in service with certain defects;
If it were a protracted strike...
No train planning/diagramming staff to produce amended timetables etc,
No commercial staff to plan and release advance fares
No safety staff to maintain compliance with safety legislation
No HR staff to deal with recruitment of new staff so potential frontline staff shortages
Basically, if they're rail employees and not a director or a frontline member of staff (other than ticket office staff) they'll be represented by TSSA.
The problem with a TSSA strike is traditionally it's TSSA members that are parachuted in when RMT or ASLEF go on strike as they've generally come from the 'shop floor' originally and may already have existing competencies. It would be rare for an RMT member to be drafted in to, say, staff a control room, or perform on-call duties, simply because they don't have the level of training required to do that. Therefore it relies on non-union management and office staff to cover these roles in the event of a strike - traditionally TSSA has a lower proportion of eligible staff as members than the other rail unions, but even then in the more specialised areas you tend to find membership is higher.
There is unfortunately some thinking in the industry that the railway runs simply by a driver getting on a train and a signaller making the signal go green, when the reality of it is there's a lot of prerequisites that need to be in place for that to happen, and those prerequisites are what primarily TSSA members deal with. For what it's worth I don't think TSSA members would vote to strike nationally on this particular issue. Indeed most TSSA members are currently dealing (ie, spending most of their waking hours) with how to try and get the railway back on its feet again, not the opposite.