I am going to suggest a reframe of the entire question.
Before addressing the question of what the earliest cursors looked like, I want to ask what the cursor represented. From the very earliest text editors, there was some ambiguity as to whether the cursor, (usually called the "current location") represented the current character position, or a location between two current characters.
"delete the current character" usually implied that the current location referred to a character position. Likewise "overwrite one character" implied that the current location is a character position.
But "insert a character before the current character" implies that the current location refers to a position "between" two characters, namely the current character and the one just before it (if there is one).
Text editors go all the way back to "Expensive Typewriter" written for the TX0 computer in the late 1950s. This application didn't use the word "cursor", but it had commands that suggest the current location is a character location, and other commands that suggest that the current location is between two character locations.
Next, I'm going to suggest that the block cursor and the horizontal line cursor both visually suggest a character location, while a vertical line cursor visually suggests a position between two characters.
Next, I'm going to note that the early "glass TTY" style terminals had no way of putting anything between two character cells, but could put a cursor in a character cell. This argued against using the vertical line, given the above discussion.
The early glass TTY terminals were produced in the 1968-1970 timeframe. DEC got into the fray with the VT05 terminal, eventually superceded by the VT52 and the VT100. All of these terminals required a cursor in a character location, and not between two character locations. AFAIK, they all used either horizontal line or block cursors, sometimes user selectable.
So the answer to your question is that probably no large scale manufacturer of glass TTY terminals used a vertical line cursor. But this is only guesswork.