I'll explain it from the start, even though you probably know some of this already. The period of a pulsar is the period of its rotation, so how fast it rotates. The "p-dot" of a pulsar is the speed at which the pulsar period decays over time, how quickly the spin rate slows (since everything is always slowing down). And so this is why you wouldn't need a calendar, because by observation, you can get both the period of the pulsar, and the pulsar's p-dot (just by measuring the period a handful of times and doing the math). So ET wouldn't need a calendar, they'd just need to have cataloged the same pulsars in at least a few different sky surveys. Or at least once, because if I gave you a period value of 0.34567890 (hypothetically ignoring units), this is enough information to reduce to the total number of candidate pulsars to one. Unless you want to talk about enormous time scales (e.g. millions of years), but then you'd still be able to reduce the total number of candidates to a handful since pulsars have wildly different periods (and p-dots).

So this is actually how the map "encodes" the launch date of the Voyager probe (and how I was able to change this data and encode my own birthdate in my tattoo): We measure the period of a pulsar at a specific point in time. The pulsar above with period 0.34567890 is a specific period that will change over time due to the natural slowing of its spin (it's p-dot). So all the periods "encoded" into the original map were December 1969. I identified the pulsars, updated the data (distance, direction) with data from the new sky surveys, then advanced the pulsar period value by the p-dot value between December 1969 and the precise date of my birth, then re-encoded those new period values into binary, placed them on the "new" map with updated direction and distance data, and got the tattoo.

I discovered all of this stuff in the research phase of my tattoo. I had some discussions with a handful of professors in the Astronomy department at UH -- where I was going to school at the time -- and for a time it became this "thing" that was well-known in the department. I'd go visit someone for the first time casually during their office hours and they'd mention they'd heard of my idea. Probably one of the best compliments I ever got was from an old engineer that had worked on the SSME (Space Shuttle Main Engine, one of the most complex machines ever made) who said that my tattoo was the nerdiest thing he'd ever seen. Felt good man.