The critical regulatory language pre-9/11 was in FAR
121.547(a)(4) "Any person who has the permission of the pilot in command and is specifically authorized by the certificate holder management and by the Administrator.
For those of you outside airline flight ops, the "certificate holder" is the airline and the "Administrator" is the FAA Administrator. So the way the certificate holder defines who can jumpseat is they write an operations manual which includes their jumpseat policy. The Administrator in the person of a FSDO that "holds the certificate" of that airline has appointed a Principal Operations Inspector or POI who accepts or does not accept the airline's jumpseat policy. At some airlines that policy was written and FAA accepted to be no more restrictive than the language in the regulation above.
In the golden days before 9/11 the FAA did not really mind so long as safety was not compromised in any way. Company management might not mind as long as safety, profit and propriety were not compromised. Taking your girlfriend on the jumpseat was an unlikely event on a revenue flight!
So if an airline had a fairly non-restrictive policy, you could ride jumpseat as long as the captain did not object, your name was on the flight release (which is how the company "specifically authorized" you. You got a briefing on the sterile cockpit rule, emergency exits available to you, use of your oxygen mask and anything else the PIC felt worth mentioning and you were off on a little adventure.
Happiness is not seeing another trite Ste. Maarten photo all week long.