Apple make this difficult. Of course.
If you cut off the Magsafe 1/2 plug, you have only two wires (as well as a lot of corrosion because their non-standard plastic eats the copper in the cable). You only measure a few volts across them, what's going on?
The power supply outputs a few volts through a high value resistor. It waits until an exact resistance is seen across the power lines. Then it will switch on the full output voltage.
To fool it into switching on, simply put a 47k resistor across the power lines. This seems to get it to output about 16V.
But there's a problem! What if the brick is already connected to a load? It won't see 47k any more, since your load is in parallel. You could unplug it and plug it back in again. But that's a lot of trouble.
Instead you can add a P-channel MOSFET like this:
S D
Charger brick + -------+--------+--------+-+ +------- Output +
| | | ^ |
| | | | |
| / - - -
0.1uF --- 15k \ ----- IRF4905
50V --- / | G or other
| | | P-channel
+--------+--------+ 10A+ MOSFET
| that switches
/ on fully with
33k \ 5V gate-source.
/
|
Charger brick - ----------------+------------------- Output -
The Macbook charger can output up to 20V, but I don't know what triggers it to do so. If you draw more than a few amps?
This probably won't work with the new Magsafe 3 rubbish.