Are all signals fitted with data recorder equipment?
No. Signals themselves are not normally fitted with any data recorder equipment.
Can I rephrase your question, ‘Are signalling systems fitted with data recorder equipment?’.
Some. It depends on the type of signalling system. And if the type does not record data as standard, if the powers that be decided to fit a ‘condition monitoring’ or ‘data logging’ / ‘monitoring system’.
Computer based interlocking signalling systems record a record of every event seen by the system.
Some remote control systems (a digital transmission system known in the industry as a Time Division Multiplex or TDM) where the route relay interlocking is remote from the signal box / panel / PSB can also record all transmissions in both directions (‘commands’ and ‘indications’).
Some other equipment (for example, such as computer based axle counter systems, HPSA point equipment) also logs data. However not all have a built in real time clock (RTC) as standard.
Also, not all systems are connected to a remote ‘server’. So some have to be visited by staff to get physical access to the system.
The time resolution depends on the system. A lot of systems have a resolution of one second.
Please note that there are many variations, so just knowing the signal box type is not always going to help. However modern signalling centres (regardless of what they are called) are very likely to use a computer based system.
Here’s a selection of photos:
SSI Technicians Terminal:

The system logs most (but not all) faults where it can detect them. It is also possible to examine the data from the live system. Additional equipment can play back the recorded data.
ATP Encoder

Very limited information is available, as it can only detect some types of faults. As it does not have a RTC it can’t say when a fault occurred.
HPSA handset (for points)

Again, limited information is available, as it can only detect some types of faults. As it does not have a RTC it can’t say when a fault occurred. Additional equipment can however send the data to a remote system, which does record the date and time.
SA380C data logger

Used to record the state of important relays, such as signal control, point control, level crossing control or track circuit relays.
VAMOS Level Crossing Equipment

As you can see, it can detect some types of fault. It has a mobile telephone data link to a remote system that records the data.
Within S&T, the term ‘destructive testing’ has a very specific meaning. It only applies when S&T staff are investigating a wrong side failure . That is, where an allegation has been made that the signalling system has or may have operated in an unsafe mode or manner. Signalling equipment is designed to fail safe, that is, every reasonable effort is made to design the equipment so that if/when it fails, it will fail in a mode where it’s self protecting. Hence if it fails on the wrong side of this, it’s failed the wrong side (the/a unsafe side) and hence trains, or other users (level crossings, railway staff) may be put in danger.
Officially it’s part of the signal failure investigation which is part the Signal Maintenance Testing Handbook (SMTH).
There are three stages to an investigation. First is the non-destructive part. This is evidence gathering, visual inspection of the signals controls (levers, buttons, switches or equivalents) and indications, visual inspection and examination of relevant equipment (signal(s), point(s), relay(s), cables, plus much more), downloading data, taking voltages. If any part of the non-destructive work may disturb the equipment, it’s deferred to the ‘destructive’ testing.
If the cause has not been found, then permission must be obtained before proceeding to the ‘destructive’ testing. This is where the equipment has to be disturbed in order to carry out checks and tests. It includes checks where wiring has to be disturbed, and where the equipment is operated to see if the fault can be recreated, to check how the equipment operates, to electrically test the insulation of the cables and wires, plus much more.
Lastly consideration is given to anything else that may have caused or contributed to the symptoms seen / reported.