First it is necessary to understand the principle of timekeeping. The underlying principle is that the measure of time is the event.
Events take time. Therefore the number of successive events gives you the measure of time.
The brilliant, celebrated, and lamented Piet Hein wrote:
Eternity's one of those mental blocks
The concept is inconceivable
My clock digests it with ticks and tocks,
Belittled, belaboured, believable.
Each passing moment is seized and chewed
With argument incontestable.
Premasticated like baby food,
Eternity is digestible.
The principle is simple: either you find a process consistently slow enough that it will not run to completion, but with its progress remaining measurable after the desired period, whether that period is to be milliseconds or tens of teraseconds (which is what you would need for 1 million years) or petaseconds, (which is what you would need for the age of the Earth.
I ignore for the moment the question of what would be intended to prompt the archaeologist to suspect the intention behind your timekeeper.
There are in fact many notionally adequate timekeeping principles, some more practical than others. In our day and age, one immediately leaps to isotopic options, and certainly they have their attractions, but the most obvious approaches would be pretty expensive. Suppose you began with samples of defined combinations of isotopes (an appallingly expensive demand immediately!) decaying at different rates, and selected for suitable half lives. If it occurred to the archaeologist to analyse the sample for isotopic content, then it should be very easy to signal that timekeeping was intended. For example blocks of noble metal or synthetic rock, containing long-lived isotopes of technetium, neptunium, curium, and other isotopes not occurring in significant quantities in nature, would clearly signal their synthetic nature and would remain usable timekeepers for millions of years.
By thoughtful inclusion of still longer lived isotopes, one could extend that period to billions of years in the same timekeeper.
Note that isotopic ratios need not be the only readable traces remaining. Such things as charged particle tracks and thermoluminescence could provide powerful clues, especially in combination with other effects.
However there also are totally different processes that would permit a technologically savvy archaeologist to make an intelligent estimate of elapsed time. The rate of flow of a viscous substance (not ordinary glass! Stories of flowing windowpanes at ambient temperatures have been as badly exaggerated as Mark Twain's death and Elvis's survival.) Some organic materials would seem attractive, though I am sceptical. The molecules of such substances have nasty habits of cross-linking into solids over really long periods.
Again, one could store a volatile solid such as anthracene or iodine at a depth where one could neglect changes in temperature. Stored in say, argon, in a coiled tube with baffles at intervals along its length, the percentage of material that had redistributed itself down the years should give a very good basis for estimation of elapsed time.
A prettier process, possibly even more effective, might be to seal a chemically stable, colourless, transparent inorganic gel in a long tube. At one end it could contain an intensely coloured simple salt of higher density than the gel, possibly trivalent chromium. The distance that such substances diffuse varies roughly with the square root of the elapsed time. That may not sound very impressive, but given a column a few metres tall, you might be startled to calculate how long one would have to wait before the concentration gradient began to level out.
One possible medium would be ice, if you could be confident of maintaining a suitable temperature.
Erosion of massive blocks, or the growth of "desert sheen" or "desert varnish" on a combination of rocks of a suitable nature and shape, might also work well enough for many purposes.
There are other approaches, including digital ones. Let's get back to radio isotopes. (There are alternatives, but that is a discussion that could keep us going for many pages.) Choose isotopes that will go on delivering sufficient power in excess for a sufficient period. This should not be terribly difficult or expensive.
Use the isotopes, by whatever technology proves most convenient, to generate electricity. The process need not be particularly efficient, since microwatts should be plenty. All the electricity need do is to drive a visible, sealed counter with magnetic bearings. It does not matter whether the archaeologist can read the numbers on your counter or not. Once a day or once a second or at whatever frequency you prefer, the counter adds one to its total. Suppose you wished to count to 1,000,000 years one second at a time, your counter need only have about 14 digits. If you prefer 1 billion years, 17 digits should suffice. Work it out.
Perhaps you are nervous of mechanisms with moving parts. If so then you could use rather massive electronic counters, with plenty of redundancy in the face of recrystallisation, cosmic rays, electromagnetic pulse and so on.
Alternatively simply take rods of suitable materials and place them two by two in contact end to end. If you have chosen well and kept them in a suitable medium such as argon, Their atoms or molecules will diffuse into each other, very slowly.
An example of suitable rods would be gold and silver. They are noted for diffusing into each other. Mercury also might be useful in this way.
If you will not limit your archaeologist to terrestrial environments, there are many options for orbiting time capsules, but by this time I am sure that you have enough to go on with.
Let me know which mechanisms work best. And don't be discouraged too easily; your ancestors did fairly well by scattering used cosmetics and rocks where they would be found. Frankly, they did better than our modern data storage technologies promise to do...
Cheers,
Jon
