Ok, even if I couldn't see why it should work just by installing an app I did a clean flash of your Rom without Google apps and installed only zarchiver.
But as expected that didn't change anything. The program runs fine (no error report whatsoever) as do all other apps but the EXTERNAL sd card is just not shown - it probably is not mounted by the system at startup! Unfortunately I have not the expertise to fix this by editing some startup files with an editor. Probably it is only a minor setting which will make it work...
Back in the recovery I did a complete backup of your Rom to the external sd card with works perfectly there! So next time it should be easier to quickly change to your Rom to test something.
But first you need to fix the external sd card mount problem. I can't believe I am the only one experiencing this. In all other roms the external sd card works fine...
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