Monitor Output, for 24p

That would depend on your camera since that's where you are converting the digital video signal to analog video in order to monitor.
What camera are you using?

The GL1 records at 29.97 fps so that's all it's going to pass in real time.
You might be able to use 24P material with playback set at 29.97 as a custom setup.

I've never tried that, I'm using a capture card that lets me do what I want

I don't think your going to get what you want in SD with that setup. 23.98 is what might be supported by the sony but doubtful over s video. there are not a lot of monitors that support 23.98 and when they do it's usually over component and it's usually an HD signal.
FCP will let you do an NTSC DV @ 23.98 for offline purposes. It's not a supported frame rate in NTSC Standard def. 29.97 is it.
You can create SD DVD from 23.98 sources but the DVD player is inserting a 2:3:2:3 cadence to 29.97

AJA Kona products are what I use. Kona 3 on my box, LHe on another, ordering LHi for another and an old i/o on a SD only box.
There are several choices from other manufacturers as well. If you see one you think might suit your purpose check the hard tech specs for what it will do not the marketing ploys. check around the cow forums, this forum and others for problems/solutions.
What were you monitoring on set with that monitor at 23.98?

the XL2 can shoot 24P or 24PA but the signal is recorded and displayed at 29.97. the 24P cadence is 2:3:2:3 while the PA cadence is 2:3:3:2
you were seeing 29.97 video not 23.98
from the specs on the box you asked about
"PYRO A/V Link Specs:
Capture Resolution:
NTSC: 720 x 480 @ 30 frames per second"
of course they mean 29.97 no mention of it's ability to play back 23.98 SD

you can view your 24P material on your computer monitor.
What is it you are trying to accomplish and what are your deliverables?
that will determine your course of action.
If you are not going to master to an SD tape based format, and are cutting for web or SD DVD delivery your computer monitor will suffice.
If you are going to master to tape and release in SD stay at 29.97 since that's what you will end up on in an NTSC SD world.
The whole intent of 24P in standard def is to mimic the effect of shooting on film and transferring to video. It's a look.
The only reason I know of to use 23.98 SD is if you are off lining a project where the source footage is too demanding of a small system to work with, and be able to match the frame rate. Even at that DVCProHD at 23.98 would be better suited for that workflow.
Then again I'm an old guy and that's the way I think

http://www.aja.com

If you previewed it with the video output of the camera, you're seeing 29.97 video. Most SD cameras that shoot 24p are actually shooting 29.97 with a pulldown flag that allows fcp to remove the pulldown. Your seeing this 29.97 fps vide.

Don't know. As Tallguy suggested, you might want to investigate some of the AJA or Matrox products and see if they can do it. You might also just next your 24p sequence in a 29.97 timeline. My understanding is that fcp will not do a great job of adding pulldown (so it won't be perfectly smooth) and I have no idea if it would be in realtime, but worth a shot.