The independent Bear and Bull market for altcoins is quite difficult to determine. While it actually exists, Bitcoin normally sets the tone for the overall market. So if Bitcoin is experiencing a bull market, the altcoins suddenly seem to have an increase in demand hence an upward price movement. The same case when it's a bear market; Bitcoin goes down, and altcoins start to nosedive (some even get their new ATL in the process). The last bear market is an example. However, this isn't the same for all altcoins as some altcoins with solid fundamentals, unique features, strong dev teams, etc can have a positive market while others are bleeding.
A valid question that the OP asked, because it is only bitcoin bull and bear run that most of us know about. From your analysis it is understandable that bitcoin is the pacesetter while other cryptocurencies follows, so in this case altcoins follows bitcoin trends. So i think that bitcoin bull run will trigger the interests for altcoins, where investors will also want to cash in on other forms of crypto coins. So this can be s sort of bull run also for altcoins, I'm guessing that when it's bearish run for bitcoin, then it'll also affect altcoins negatively. It's just speculations for me, because like the OP I've not come across where we're expecting bull or bear run for for altcoins, unlike bitcoin that has its pattern.
I believe that there are altcoins out there that can have their own bull and bear seasons, but since my interests are not in altcoin, I wouldn't know much about them. I really think that if there is a sort of regulation for altcoin development, and we don't have plenty of them, then we can understand and predict their seasons better. But crypto is decentralized, so it's easier to mix valuable coins with worthless coins together as altcoins, making it quite difficult for investors to have trust and know their trends.