Edited, as suggested by omegaslayer.
I found the answer here:
http://www.hl2world.com/wiki/index.php/Dynamic_Lights
If you follow that guide you just have to do some minor tweaking to get the result I desired.
If anyone wants to know how to make a light that hangs between two cables... this is what I've learned:
You have to create a move_rope entity and then a keyframe_rope at the
point where you want the light to be hung. Then you create
another keyframe rope opposite the move_rope entity. You make the
middle keyframe_rope the parent of the light prop you want to use, and
then you make the light prop the parent of a light_dynamic. The
light prop should also be a prop_physics_multiplayer. Also, you
need to add phys_pulleyconstraint for both segments of cable to keep
the light from dropping to the ground in game. For the first
segment of cable the phys_pulleyconstraint should have the first entity
as move_rope, and the second as the light prop (you have to name all
your entities in order to fill in these two fields). For
the second cable the first entity is keyframe_rope and the second is
the light prop. Messing around with the slack settings on both
cables will obviously alter the amount the light prop hangs and
stretches when shot. You will probably need to mess around with
the settings of the light_dynamic in order to make it look
convincing.
In the end however, I've decided the light suspended by two cables
hanging in the middle just looks hokey no matter you do. I'll
stick to different lighting methods in the future.