There are two likely possibilities to how the ambulance communicates with the ER (via radio). They may be calling on the VIPER network or since the county is all on VHF, they could be using the conventional HEAR channel of 155.3400 (110.9 PL). Both of which are in the database and should show up on the HomePatrol. The latter of the two will be more difficult to bring in because the radios are simplex and operate in line-of-sight, so you will not hear any traffic unless you are within a mile or so of the ambulance. If the hospital is transmitting from a tall location then you might be able to hear them reply.
There is also a chance that they give patient information over the phone, or if they are busy, the driver will contact dispatch so they can alert the hospital for them.
Long story short,
Keep all 10 MED channels in your PSR600, 155.3400, 155.2200, 155.4000 (all with no tone), and keep a wildcard open on the local VIPER site and you should hear some traffic at some point.