Minimal components for timer relay
There are many low-cost approaches for solving this problem.  I will list the two that I would consider:

1) CD4060 (or 74HC4060) timer / oscillator.  These chips cost several pennies from Asian suppliers.  A few resistors and a couple of capacitors are required.  Probably may also need an output buffer for the LED, depending upon LED current.

2) 6-pin Microchip PIC.  These are also available for very little money, although my favourite part from that family (PIC10F321 or 322) does cost a bit more.  The chip can directly supply up to 20mA or so to the LED, so a buffer may not be needed.  Again - depends on the LED.  You can also feed the LED with multiple pins for more current.

Still need a couple of resistors and a couple of capacitors but otherwise very simple.

The PIC-based solution is probably the most flexible and would also have the smallest footprint.  You could literally fit the whole circuit on a PCB the size of a postage stamp.