In the diesel the engine mounts are vacuum controlled.
I believe the gassers don't and use rubber mounts filled with hydraulic fluid. If that's the case they are easy to spot as they are covered with fluid that looks (and taste, if you'd ask) like coolant.
Now back to the diesel mounts. It may have to do with the vacuum system since when you step on the break you activate the vacuum assist system.
Take a look starting at page 100 of this document ->
https://drive.google.com/file/d/0B1e...ew?usp=sharing
Your vacuum system *may* be somewhat different but it should give you a general sense.
Another member of this forum by the screen name of
ninja_zx10 was looking at engine mounts as a possible source of vibration, but I'm not sure if he ever solved it.
It could also be total unrelated, but since the topic of mounts came up, I thought I'd share what I know about them.
As always, we appreciate if you report back any finding for future reference...