OK, I've just spent a week in 'deep discussion' with the Azerb. embassy in Tbilisi in regards to this very problem I've also encountered online. Basically, they insisted for 6 and a half days that nooooo, there are no restrictions for motorbikes and that they'd never heard of this '72 hour rule'. But, of course, it's all over the net, so I didn't budge
Anyway, the good news is that I was right
the bad news is that I was right
Due to an idiotic mistake (literally) made by whomever wrote the law back in 2004, when it mentions that foreign visitors entering Azerbaijan with their own wheels are free to drive for the duration of their visa (15 or 30 days), they specify cars but NOT motorbikes. the consul assured me this was stupid and that of course bikes are included, but it does not say so on paper, and that's all that matters.
The good news is that 'overstaying' incurs a very low penalty fine (about $30-40) and the Consul actually ADVISED me to overstay and pay the fine. Go figure. To pay the fine you must show up at the customs on the port in Baku, they will give you a fine slip, which you will take to whichever office they tell you, pay the fine and return to embark the boat to Turkmenistan.
However, be careful to go with hours if not a day to spare, because this office is back in town centre, and people caught unaware missed the boat by the time they got back. the next was cancelled, they overstayed their Azeri visa, the whole thing was a mess
Option 2: Get to Baku and head to port, park your bike in customs within 3 days of entering the country and forget about visiting the rest of the country with your own bike.
We are planning to cross into Azerb. on the 14th March (in 10 days) and are wavering b/w the two options. partner wants to overstay but I am sceptical. I have yet to knowingly abuse a law in 10 years of overlanding and never had an issue. Anyway, I'd be happy to post update if you like??
If it all goes awry, you may need to delete expletives after I've posted
Cheers for now