TinyCore is great, brilliant...
BUT you have to know a few tricks to make this simple yet persuasive Distribution work for you...
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Don't trust the Apps engine to download the right dependencies - in fact, you can't even trust the people who make the .tcz files as sometimes they have .tcz's "installed" and don't realize that you'll need them too (see my tinycore filezilla install tutorial)...
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Manually copy things and manually edit the files.
Mounting the tiny_core iso and copying the kernel & initial ram disk to a directory is the most effective way of "installing" tiny core. Then creating a few directories, manually adding a GRUB entry...
Similarly, download (or copy) the .tcz files into your /optional directory. Then, if you want it available modify the onboot.lst (first make a backups, then very carefully! no extra spaces or lines).
Then reboot and see how robust the system is (fast boot, everything loaded, appears in the menu).
/opt/.filetool.lst (lists the files backed up by the filetool.sh -b app to persistent disk)