From personal experience I use power, hr and how I'm feeling to determine a rest week. This recently led me to switch from a 3 on 1 off 4 week cycle to a 2 on 1 off 3 week cycle.
Obviously power is the goal and declines when I'm accumulating fatigue. Resting HR generally goes up and I can't get my performing HR as high when I'm feeling tired. RPE creeps up leading up to a rest week. All three combined point towards a rest week for me. That being said, I have made some recent changes to things recently as I found I was kind of trapped in the mindset of following the formula rather than listening to these signs.
The reason I did the rest week on the the 4th week was simply I just thought that is what you did. However, I have always found the 3rd week felt like I was scraping the bottom of the barrel in terms of fitness. Power would be down, HR would be less responsive, RPE would be up, and I felt obligated to stick it out rather than motivated to do the work. I also found on that 3rd week I would become a grump around the house and not necessarily the most patient father or partner. I started wondering if maybe I was going too deep in that 3rd week and not really recovering properly in the 4th week.
Watching one of Sieler's videos where he discusses his daughter's training and they talk about the switch from a 7 day cycle to a 9 day cycle. It opened my mind to different cycles based on how I respond. I had already switched to polarized and increased the number of Sieler Z1 days but still that 3rd week had me feeling hollow. So I decided to follow the signs rather than the formula and switched to 2 on, 1 off.
The switch to polarized and this new cycle initially felt like I wasn't going hard enough which tempted me back to my old ways. However, as I started feeling fresher overall I was hitting higher heartrates on my hard days and then the PBs in power started coming. I felt like I was able to go harder and noticed on my powermetre that in fact I was.
The other thing I noticed is my Sieler Z1 work got faster at the same HR. For efficiency/effectiveness I run on my Z1 days because I live in a rolling hilly area which causes the riding to be very stochastic and difficult to stay in a specific zone. Running makes it easier. Going easier more often and reducing the amount of intensity eventually led my pace per km almost a minute faster in Z2 HR (Sieler Z1). In terms of power and HR. I use Xert and my LTP has gone up. When I am around but under LTP my HR is in Z2 which confirms the increase power at the same HR. In other words I'm getting faster for the same cost.
Still, at the end of the second 'on' week power would decline, HR would be less responive, and RPE would increase. I take this as a sign to cut the intensity out but keep the volume consistent - I go easy on the usual hard days. During the rest week I'm careful to keep the power down and stay within the lower HR zones. I look to RPE as the indicator to how the week is going. I find RPE comes down throughout the week for the same efforts as the beginning and I started getting the itch to go hard again. The power targets are easier to hit, my HR becomes more responsive, and RPE feels easy.
What does this all mean? Breaking away from the formula to using power, HR, and RPE combined are the best ways to determine a rest week. You can also use these 3 factors to determine if your rest week is working, and when you're ready to reintroduce some intensity. This is all done under the umbrella of polarized training.
Granted this is all from one individual so I'd take it with a grain of salt. I only hope my experience helps someone out and speak solely from personal anecdotes as I'm a financial analyst, not a sports scientist
*EDIT* One additional note: I have two young kids (oldest is 3) and don't get a lot of sleep. My HR relative to my pace is pretty consistent for my runs even with a bad night but my RPE can vary quite a bit. During the hard riding efforts that HR varies more depending on my sleep.