🚀 go-pugleaf

here is a guess... 
Looking at the components you suggest I could make one that should work. 

put a resistor, and LED, a Zener, and an SCR in series. The Gate of the scr
goes through a resistor and a pushbutton to + phone line. Lets draw a 
schematic online... (Hope this works)

-----------phone line + -------+-------------+
                               |             |
                               R             |
                               |             |
                               \___PB_______SCR
                                             |
                                           \_|_
                                             Z  \
                                      +------|
                                    \_|_     R
                                      Z  \   |
                                      |     LED
                                      |      |
--------------- phone line - ---------+------+

The SCR is off until pushbutton PB is pressed making contact thus
turning it on. Upper Zener is some voltage higher than the off hook voltage
of the line. (say 10 volts)
Until the line goes higher than 10 volts it is off, even though
the SCR is on. Hold the push button as you hang up. This turns on the
SCR and as the line voltage rises the zener conducts and the current 
through the SCR will hold it on (get a low hold current scr, say 3 ma)
The resistor in series with the push button supplies the small turn on current.
5 k should do.  The lower zener limits the voltage across the LED. Make say
5 volts. This would put the r in series with the LEd at about 150 ohms.

Like no guarantees...