I promised to write this up if successful, so here it is.
There was a LOT of experimenting, primarily on the GUI installed 32-bit Core system, with the xvesa default GUI interface. Nothing I tried was successful. There might be a way, but I never found it. I admit, I'm not the linux gearhead that tinycore seems best suited to. Tinycore's reliability and forgiveness (you can start over easily) is unmatched, so its worth some effort.
I finally decided to see if Corepure64 (vs 32-Bit Core) would provide a solution.
The following worked. It's easy, as are all solutions once you have the answer.
First of all, make sure you have an internet connection. Mine is cabled, but wifi should also work.
There are subtle, but important differences in the install options between the 32-bit installer, and the 64-bit installer. For example, wifi can be added as a part of your base install on the 32-bit install options. The 64-bit install logic does NOT include an election to install wifi as a part of the base build. If you need 64-bit wifi, the topic referenced in 2) below contains a how-to for wifi on 64-bit.
1) Build a text based, CorePure64 using the INSTALL GUI from your ISO media. This is the most basic setup.
a) Boot Core with X/GUI (TinyCore) + Installation Extension
b) Select the tc-install icon from the GUI choices
c) Select Download From Internet, when asked Which architecture? select the 64-bit button provided
d) USB-HDD (my core goal), Whole Disk is selected by default, and select the removable disk you want to build your system on
e) I went with the default ext4 format and NO additional Boot Options
f) This step seems to be important: Select: Don't install Extensions (Core Only, Text Based Install)
g) Proceed button to build the base system
h) Exit and reboot, removing your ISO installation media.
2) Here's the key, from a topic in the forum: Topic: [Solved] How can corepure64 support GUI?
http://forum.tinycorelinux.net/index.php/topic,24093.0.html If your WiFi is working you can use these commands to get a gui: $ tce-load -wil Xorg-7.7 flwm aterm wbar
$ startx
3) At the text interface presented on the new 64-bit tinycore system:
tc@box:~$ Load these options just as described in Juanito's description above in step 2).
I used
tce-load -i -w Xorg-7.7 flwm aterm wbar to make the GUI part of my boot, not temporary (my understanding of the "l" parameter).
4) From the new GUI, search for and install libreoffice.tcz from the extension library for 64-bit tinycore
This installation properly displays a blinking caret at the location of the cursor on a Libre Office Writer document. The caret is a vertical line, roughly equivalent to the | "pipe" character on your keyboard, located at the text insertion point on your page.
Please note:
I went through the steps above TWICE to make sure I got the same result.
I went through multiple iterations of the 32-bit installation,
INCLUDING the above steps, but never succeeded in getting the blinking caret I was looking for.
Hopefully this can help anyone else trying to achieve this result. I intend to further tweak the system over time, but this base behavior was my non-negotiable stating point.
Please mark this solved, or provide instruction for how I can do so.