Live plant as a touch switch
OK, we're engineers not biologists but entertaining a child is a worthwhile endeavor, so here's what I'd try:

Wrap the stem of the plant with foil (copper tape or aluminum foil), putting the touch plate wire inside that wrap. This will couple capacitively to the vascular channels that run through the plant. Don't stick the wire in the dirt, that just adds a large undesired capacitive load.

Give the plant a generous feeding of liquid fertilizer, one that has plenty of minerals. Don't use too much plain water either. As this new mix rises in the plant's vascular channels -- which may take a couple of days -- it should increase the conductivity of those channels, making the rest of the plant more sensitive to touch.

The touch circuit may be self-calibrating, so unplug the light and re-plug it after you've done the above.

Finally, when the child is about to touch the plant, hold their other hand yourself, increasing their capacitance to ground. Here's hoping it works!