Hello John
First recommendation is please take a look at the Core Book
http://tinycorelinux.net/book.html where you'll find most answers
Also please look in the FAQ
http://tinycorelinux.net/faq.html#pendrives referencing the section "Pendrives" to help resolve your issue
When using USB thumb drives it's strongly recommended to use the waitusb bootcode and to specify the path (partition) using UUID to the tce directory
Assuming an internet connection, at the command prompt load util-linux extension
tce-load -wi util-linux.tcz
Determine the identifier of your USB drive
tc@box:~$ blkid
/dev/sda1: LABEL="SYSTEM" UUID="DE2F-EF34" TYPE="vfat" PARTLABEL="EFI system partition" PARTUUID="bb9fe922-8e60-4124-a783-8a9fe7ffd786"
/dev/sda3: LABEL="OS" UUID="963C32313C320D2D" TYPE="ntfs" PARTLABEL="Basic data partition" PARTUUID="4ea8fcda-a776-4473-a0ec-8751506eb525"
/dev/sda4: UUID="2E4EEC924EEC53DD" TYPE="ntfs" PARTUUID="ebfd31ba-d92c-4b46-b6ac-6a363410503e"
/dev/sdb1: LABEL="BOOT" UUID="B854-8FE0" TYPE="vfat" PARTUUID="8ec4d514"
/dev/sdb2: LABEL="TC" UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311" TYPE="ext2" PARTUUID="8ec4d514-02"
...
Or if you are sure of the identifier of your USB drive containing core installation, for example if your USB drive installation is sdb1 then :
tc@box:~$ blkid -s UUID /dev/sdb1
/dev/sdb1: UUID="B854-8FE0"
if your tce directory is separately located on an ext2 formatted partition, then
tc@box:~$ blkid -s UUID /dev/sdb2
/dev/sdb3: UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311"
(Obviously use the UUID as found in your system, not my examples..)
Then edit the boot config (extlinux.cfg ?) file adding:
waitusb=5:UUID="B854-8FE0" tce=UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311"
to the append line
Extlinux example:
KERNEL /tce/boot/vmlinuz
APPEND initrd=/tce/boot/core.gz loglevel=3 waitusb=5:UUID=B854-8FE0 tce=UUID=B854-8FE0
Grub2 example:
search --no-floppy --fs-uuid --set=root B854-8FE0
linux /boot/vmlinuz tz=GMT noswap loglevel=3 waitusb=5:UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311" tce=UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311" opt=UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311" home=UUID="b313c2c4-fedf-4c44-bf42-6a6fca54b311"
good luck