Yes - a gonadotropic hormone is what I found in my searching on the internet.
Rapid growth in gonads isn't going to necessarily affect it; in germ cells, the telomeres are kept intact by telomerase. (Telomerase is also expressed in tumors of some kinds.)
The only case in which I've seen an octopus keep its pupils closed was in an octopus at the aquarium I volunteered at; this was probably partially because of the conditions in which she was kept and not necessarily due to normal aging processes, plus her keepers gave her another estimated year and a half before she died.
Surgical removal of the optic gland, oddly enough, also causes sterility in the octopus whose optic gland is removed.
If the light pattern of the day meets certain criteria, wouldn't the onset of sexual maturity occur in any octopus exposed to it? I would wager that certain other biochemical criteria would have to be met; this is much the case in mammals of certain ages whose mating season is determined by environmental criteria.
Ultimately, I guess what's not answered is why this causes the octopus to die (and interestingly to me, the onset of senility in the male octopus. What goes on in the brain of a senescent male octopus? Perhaps this could have some interesting medical applications).
For everyone's benefit, this is what Wikipedia says about gonadotropic hormones in Vertebrata (I have made it a different color because the quote function is hard to read):
Gonadotropins (or glycoprotein hormones) are protein hormones secreted by gonadotrope cells of the pituitary gland of vertebrates.[1][2][3] This is a family of proteins, which include the mammalian hormones follitropin (FSH), lutropin (LH), thyrotropin (TSH) placental chorionic gonadotropins hCG and eCG[4] and chorionic gonadotropin (CG), as well as at least two forms of fish gonadotropins.
The alternate names for these hormones are follicle-stimulating hormone (FSH), luteinizing hormone (LH), thyroid-stimulating hormone (TSH), human chorionic gonadotropin (hCG), and equine chorionic gonadotropin (eCG).