Connecting LED Lighting Tape

If its a fixed installation a junction box of some sort

Depends what you are after... if you want a longer "tail", then flex, crimps and heatshrink. For direct connection to fixed wiring, then a junction box, or other enclosure with suitable terminals in it (wago[1], crimp, chock block etc)

Would a WAGOBOX Light Junction Box be acceptable?

Are the tails single insulated or a sheathed flex?

If former, I don't know - I think I suggested to someone here with a similar question to buy the RS PSUs that don't have that stupid arrangement.

Technically you'll have to contain all the wire in an enclosure - so if it were me, I'd return it as not fit for purpose.

If it has a sheathed flex, then Wagos or terminal strip in an enclosure is pukka and fine. Even something as simple as a surface box and blanking plate with both cables clipped down as they enter (al la central heating - you'll find a lot of this if you look near your tank or pump)

Ashley terminal box would be very good:

But ultimately any junction box with strain relief OR the flex and cables being clipped near the entry points will be compliant and safe.

Thanks all - Wagobox and wago levers ordered.