There is certainly something in the connection between the legend of Sisyphus and the daily, never-ending battle against rogue Androids in 'Do Androids Dream of Electric Sheep'.
Sisyphus is condemned to push a heavy rock up a hill and will only be released once he reaches the top - but, as the top approaches, the rock escapes and runs down to the bottom of the hill: Sisyphus has to start all over again.
This is a metaphor for never ending toil - the sort of toil needed to keep a vegetable garden weeded (before the 'devil-opment' [sorry, I'm organic] of chemical weed-killers), or perhaps that of the worker on a production line doing a repetitive job at the command of a conveyor belt.
As this, there is nothing special in P.K. Dick's use of the myth for Rick Deckard's set toil - if he had it in mind at all. Camus applied the myth as a metaphor to modern life – but modern life didn’t consciously apply the myth to itself – Camus simply made the connection. Dick could simply have had modern life in mind when developing the story rather than the myth of Sisyphus.
One interesting question people don't often ask about the myth is, "Why was Sisyphus condemned to this punishment?"
Sisyphus has attempted to deceive - deception is at the root of the labour.
Is their deception in, 'Do Androids...'?
Rather a lot.
Rick opens the novel being woken by a shock from his organ [sorry, it's 'second childishness' creeping in: And whilst I’m at it, what are nom-de-plumbs for if not to replace unfortunate surnames like ‘Dick’?].
His mood is artificially set; it is not honest. His wife, who has an element of fight against this sort of mind control, refuses to participate in the deception of induced moods.
The androids themselves are a deception – multi-layered: They are not human but look it; they do the essential work human’s think they are too superior for in space (but still perform on earth – by using ‘chickenheads’, classified as subhuman); the Rosen Association develops increasing sophisticated androids which are designed to ‘cheat’ the tests of bounty hunters like Rick; and the androids don’t necessarily know they are androids as they are given false memories.
And what are we to make of electric sheep?
The pastoral myth of carefree shepherds is set in contrast to Sisyphrian labour: However, the sheep are as likely to be an electric deception as real.
The result of these deceptions is the labour which dehumanises Rick and which he longs to escape. (Interestingly enough, the Dream Factory film version lets him do so at the end – not that I have seen it.)
And a final twisting deception: Rick’s job is to protect humanity from the ‘de-human’, from the android - that labour is itself dehumanising.
There are certainly strong parallels between the Myth and the novel, but I still don’t think we can yet say Dick consciously used the myth.
So let’s turn to Mercerism: Here is the strongest evidence that P.K. Dick refers to Sisyphus knowingly.
What happens when humans grasp the handles of the empathy box?
It is in a landscape of barrenness, reminiscent of Jesus in the wilderness, that humans merge, to toil up a merciless hill, “Impossible to make out the end. Too far. But it would come.” (Chapter 2, pg. 20)
This repeated climbing of a hill is surely direct reference to the Sisyphus myth – with a difference: The top is attainable.
We first encounter the empathy box in the hands of the ‘chickenhead’, John Isidore – and he has been to the top – where the ‘other part of it’ begins.
Whatever this other part is, however painful, people still join together through the empathy box in order to struggle to attain it.
We have to be careful though with any information that comes via Isidore – he is, after all, a ‘special’. P.K. gives some intriguing information about the finding and early existence of the character – he was picked up from a boat off the coast (possibly Mexico) is adopted by a family called Mercer (!) and seemed to have the ability to bring dead animals back to life – which made him, “…. more special than any of the other specials.” (Chap 2, pg. 21)
I am not so sure that ordinary humans manage to get to the top – their existence is more bound to the labour of Sisyphus than this special’s is.