Simple question 230v to 12v 50w/5a timed output

Hi,
know a lil about electronics and electrical just want to make sure i'm not being a dummy or if there are any other better alternatives.

Problem:
A timed output circuit has gone bang on an piece of work equipment, wont go into detail as it may confuse the situation but it all works apart form the timed lamp button, I can see components on the lamp circuit disintegrated etc...
So I wish to make the lamp part sort of stand alone.
plan is to convert a 230v suply down to 12v 5a as the lamp it needs to power is 50w.

Resolution: I was going to get this

https://www.amazon.co.uk/200-250V-Halogen-Light-Electronic-Transformer/dp/B00CXK30UW and http://www.ebay.co.uk/itm/DC-5V-12V-24V-Infinite-Loop-Cycle-Timing-Timer-Time-Delay-Relay-ON-OFF-Module-/192106941494

Build accordingly and place in a project box with a push button on the project box also.

Can anyone see any issues with this?

Or am I complicating it, maybe the transformer then this?

http://www.ebay.co.uk/itm/CAR-TIMER-SWITCH-TIME-RELAY-DELAY-OFF-CAR-LIGHTS-UNIVERSAL-KIT-1-105s-10A-12V/271203168131?var=570157183343&_trkparms=aid%3D222007%26algo%3DSIM.MBE%26ao%3D2%26asc%3D46150%26meid%3D5e8c43f27aec4c1092baed675673ef1f%26pid%3D100005%26rk%3D6%26rkt%3D6%26sd%3D280890951562&_trksid=p2047675.c100005.m1851

or
http://www.12voltplanet.co.uk/12v-universal-interior-light-delay-timer-relay-10-sec-delay.html

any alternatives? advice?

Well, in the industrial area you would simply get a 240V timer relay and connect to whatever you need.
I don't know if the timer is being started with mains voltage signal or a low voltage one but these relays are available for 12, 24 and 240V, plus they come with a nice socket for easy connections and replacement.
Instead of a 12V 50W lamp I would simply get a 240V LED lamp with integrated driver ;)