Couple of thoughts on the subject:
I have worked both career fire and volunteer fire - drama goes on in every house, it's the nature of the beast.
Having worked for a county EMS agency, career, 24/48 schedule and having worked private/non-profit system status type EMS I can tell you, hands down, EMS is MUCH worse for the drama and I do believe it is because, as sexist as this sounds, the women. (Not to say that the men don't get dramatic, as they do.) By and large, the women bring much more emotional responses into the station and it shows. I don't know if in the fire service they don't let it show because it could show them as being weaker or if they just know it wont be tolerated, in any event, it seems much, much less on the fire side of things.
As far as the light issue goes, our department policy is as follows:
It is PREFERRED that you respond to the station, then the call, unless you are passing the call en route to the station.
If probationary, it is ALMOST required that you come to the station first, but this is situational dependent. (In other words, you better have a damned good reason for going direct to the scene).
If you follow the apparatus to the scene, and are not lit up, you must follow all traffic laws. If you are lit up, you must exercise extreme caution and operate with due regard.
Traffic accidents, fires, wires down, etc all require bunker gear. Since most do not carry the gear with them, they will respond to the station first to get it then the scene. Given the size of our response area (36 sq. miles) most of us are pretty close to the station and arrive in short order and typically all ride together on the apparatus to the scene. I cannot recall a situation where a member has come to the station and responded in their POV before the apparatus left the station.
All in all, if you are going to be following the apparatus and you are not lit, you should be following all traffic laws. This is just common sense - the few seconds you will save following the apparatus while they are lit is not worth the risk you are causing to yourself and others.