As a general 'rule', not cast in bronze, concrete or anything else, Dogbert617 is 100% correct.
Being retired, I have the benefit to pick just about any day of the week to travel, except, sometimes, for making LD connections or meeting with a friend or a group of riders. So I use Amsnag for all my travels unless there are specific date requirements. I've sometimes found anomalies to the 'day-of-week' rule, such as an Acela being at the lowest bucket for a 30 day period on one specific Monday when I looked in early May. So I booked it for July 8th. I just checked now, and the same train is priced at the highest bucket for July.
The NEC is a separate case, in my opinion, with multiple trains per hour between NYP and WAS. Mondays & Fridays are always the busiest for most trains, and Thursdays have slightly more empty seats, Acela and regional alike. But so is time of day. As the NEC is heavily used for business travel, the 'arrives by 10 or 11AM' and 'departs about 5 or 6PM' trains fill the fastest, making their prices head upward the fastest as well (the old 'supply and demand' rule combined with revenue maximizing algorithms).
I don't ride regional trains outside the NEC with any regularity. But I just checked the Hiawatha for July (I'll be riding that in late July) and, as expected, the early AM as well as 4-6PM departures are slightly higher most weekdays. But then, $25 or $28 seems to be the only buckets, and weekends look like $25 for all trains. Being partly subsidized by the Wisconsin, those prices are likely 'fixed' somewhat. I'd expect other regionals have similar pricing peaks during highest business travel times of day.
The once a day long distance trains are a different case, in my opinion, as most of the riders are 'leisure travel' passengers...vacations, seeing family, etc. (Although I will say that the Crescent between WAS and ATL has a high number of business riders, in my opinion...just 'count the suits' getting on or off at ATL). So, with the exception of the Cardinal and Sunset, I'd expect Fridays to be the biggest originating train days as most vacation travelers want to arrive on Saturday or Sunday and stay a week or two, and then have to be back to work on a Monday. Although I've never paid much attention to it, based on how busy things are in the diner as well as how many seatings there are (I assume that each table 'turns' once per hour), I'd have to say Mondays through Thursdays have fewer in the diner. Fridays through Sundays are the busiest.
To sum it up, if possible, travel mid-week during non-peak travel times to get the best prices. Weekends are generally lower as well due to less demand.