The light should come on when you turn the key to "on" before you crank
the engine over.  The oxy, charge, and oil lights should all come on,
then go off when the engine starts as long as your oil pressure and
alternator are okay.  Most likely the connection is broken somewhere
between the dash and the engine.  Unfortunately, the sender is under the
pushrod tube gravel guard on the left side, which is a PITA to get off.
Quickest check I can think of is to check that the brown wire coming out
of there towards the front is connected to something and if it is peel a
bit of insulation off and ground it to the engine.  The light should
come on with the ignition on.  If it doesn't, the break is further up
the circuit, so keep looking.  It is unlikely the LED is bad, but the
circuit board may be.

Have fun, and install the gauge!
--
Stuart MacMillan
Seattle

'84 Vanagon Westfalia w/2.1
'65 MGB (Driven since 1969)
'74 MGB GT (Restoring)

Assisting on Restoration:
'72 MGB GT (Daughter's)
'64 MGB (Son's)

Parts cars:
'68 & '73 MGB, '67 MGB GT