One end of the spectrum of reasonable possibilities is that evolution selected for genes that cause and or favor death the older an organism gets, through implicit mechanisms like lack of regenerative capacity, such as heart tissue, or explicit mechanisms, of which I'm not aware of any. Are there any genes that explicitly produce a timing mechanism, and thereby create a built-in notion of aging?

To my knowledge, it's all implicit, resulting from wear and tear, the gradual degradation of DNA because of the nature of chemistry on the surface of the planet, and not because any gene or biological mechanism moves an organism through some programmatic notion of mortality.

This seems true to the extent that given molecular level control of an organism, current knowledge would be sufficient to maintain lifespan to an arbitrary degree. Barring sci-fi nanotechnology, genetics and anti-aging have to figure out more robust repair and damage prevention to extend lifespan.