Just as a consideration for future designs this can be done in 1 chip
1) Arduino 328P in dip package. Use Uno dip version board to dev and program dip, ~$5
2) Or just use a Nano board, ~ ($ 2 - 3). For dev and final actual design.
This is mBlock, a block programming language where you drag and drop functional blocks, config them,
and mBlock converts that to Arduino code for you and programs dev board. Board to use is Nano, ~ $3,
or if you want to use dip chip dev board to use is Uno.
mBlock and the Arduino program IDE are free.
Advantage is timing much more exact, if Nano board used < .1% error or just chip +/- 10%. Or 1%
simple user cal routine for dip. I set LED on time for 1 sec/LED, that can be anything from 1 mS to
years. Just changing the config value for the LEDonTime variable.
Only external components, LEDs, switches, 1 R for each LED, and a cap to bypass Arduino chip (not needed if using
Nano board). Nano board has a regulator on it. You also need a pullup and pulldown R for appropriate switch.
The solution in right hand window is correct for design I think, and handles both switches.
Project attached in case you want to look at it in mBlock.
Regards, Dana.
PS : I missed LED1 and LED2 in your schematic, that would be easy to add them as well.