Reciprocal agreements seemed to be largely based on the enthusiasm and interest of the relevant person at a company. Some would have arrangements with numerous companies, I think City of Oxford back in the early 1990s had quite a few. There were also cases where big companies had been split up, but where passes were valid across both / all, even when owned by different groups. I think this was often done less for serving employees, but, in pre ENCTS days for retired staff who'd been "sold" it as a perk for their retirement. I remember the First Bristol and Stagecoach West agreement was ended when someone new arrived at one or other company, but was soon reinstated when it pointed out that it went back to Bristol Omnibus Company days when both were one company.
When I was at Western National there were always lots of requests for reciprocal arrangements, pretty much all of which were declined lest every busman and he family head to south Devon or Cornwall for their holidays. Such arrangements were reciprocal in theory, there would be more benefit one way than the other. Not directly buses, but I remember once coming back from Penzance to Bristol when there was a First Bus travel offer on First Rail and the train was fully loaded with Bristol area bus staff and their families!
Another variation was passes being valid on both operators on a joint service, but not more widely on the opposite company.
Finally, whatever the official arrangements, some drivers would accept anything. I've never used a pass incorrectly, but sometimes you'd get a conversation along the lines of "never seen one of those" to which I'd start to explain that it was valid, and be ready to produce the relevant page from our fare book, but would be cut short by the driver saying "but you're one of us, just sit down" or you'd get into conversation about where you worked, what you did, what ticket machines you used etc etc.