Unfortunately, age is very difficult to guess and somewhat irrelevant when trying to determine how long (much longer) an octopus will live. Not unlike humans lifespan varies quite a bit with biologics, eating habits and habitat. I tend to classify them as hatchlings (primarily seen when tank born, rarely in the wild), very young (not sexually mature), adult (older than 5 months - give or take), senescent (at life's end). Below are my "go bys" from personal observation and journals of captive animals. They are not fast rules but may be somewhat helpful in trying to guess.
As a general "go by" (there are always exceptions) I classify a very young animal to be dwarf sized, be benthic (some are at birth), have a full set of full chromatophores and adult arm:mantle proportion. The
skin is often translucent, males will not yet curl their third right arm and they are extremely shy, often nocturnal even for diurnal species. Very few wild caught are in this group unless they were a by catch of a live rock harvest.
My definition of adult would be somewhere after 5 months but before senescence. This is the age range we usually see when they are first introduced to the aquarium. If the octopus is male, it will clearly keep its R3 arm curled most of the time. If the species (and individual animal) has enlarged suckers on the male, these will be present. The animal will show the widest color and skin flexibility range. When white, the color is very crisp and not gray. The arms are muscular and taunt and the mantle is well controlled. This is also the most curious time and it is clear they are observing their outside world. It is also the age where escape is most likely. Females, depending on the species will start to show a thickening mantle as infertile eggs begin to develop. If she has mated she will fertilize the eggs when she begins brooding (guestimating about 8 months but again species and individual dependent). She will lay eggs and brood whether or not she has mated but
may brood later if she has not been exposed to a male after sexual maturity. Signs that she is about to brood will include finding a suitable den (she may move from her existing den and try several others), moving rocks (
sometimes not small ones) and
loose items into the den area and eating more heavily than before. Removing the eggs does not seem to reverse the brooding behavior (
based upon one attempt and a few odd notes of others experimenting)
Senescent animals are nearing their end of life. It is unclear when it begins (technically probably with sexual maturity since the two are related) and the beginnings are clear in some animals and almost overnight in others. The appetite usually dwindles to eating as seldom as once a week and much smaller portions when it eats more often. The muscular arms become sort of squishy (if you have physically interacted with the animal the difference is quite noticeable in touching the arms but also somewhat visible, something like an athlete that stops exercising). Very often the arms will corkscrew at the ends when the animal is hanging on the tank wall. Color change is very limited and splotchy and the animal will often display a grayish white. The mantle may be difficult to control and will be seen to bob rather than showing muscular control (especially true of post brood females who survive the hatchling event for a week or more -- rare). Eye sight is diminished and nocturnals may stay out in the daylight (this usually only for a day or two before they are terminal). Senescent octopuses tend to do odd things and seem to forget what they intended to do.
Here is a post and a couple of videos of KaySoh shoveling sand from one side of the tank to another. Dementia is not just for humans.