Here is an an old thread on them.

Chatgbt said:

"The Vintage Titleist Sc Bulls Eye John Reuter Jr. Design Origina and other John Reuter Jr. Bulls Eye putter listings (e.g., Acushnet Bullseye LaFemme John Reuter JR Putter 33" RH, Acushnet Bullseye O-Set 4 S John Reuter Jr. Putter 32.5in) owe their origin to the original Bulls Eye design by John Reuter Jr.

Here is the production history and approximate dates:

History & Early Production:
John Reuter Jr. trademarked the “Bulls Eye” putter on March 15, 1949, after earlier trademark activity in 1947. He began selling it commercially from his shop first in Sault Ste. Marie, Michigan and later from Phoenix, Arizona after 1950.

The original Bulls Eye design was developed and produced in the mid-to-late 1940s, with early examples from roughly 1945 onward.

Acushnet/Titleist Era:

In 1956, Reuter signed a contract with Acushnet (Titleist’s parent company) giving them marketing and later production rights.
Acushnet/Titleist began advertising the Bulls Eye putter in January 1957 and production expanded under their ownership.
The Acushnet Company purchased Reuter’s business outright (often cited as 1960–1962), after which the Bulls Eye was manufactured and marketed under Titleist/Acushnet.


Marking/Model Timeline (for aged estimation):
1957–1960: Putters are marked “John Reuter Jr. Design” and Bulls Eye.
1960–1974: Marked “Designed by John Reuter Jr.” or “John Reuter Jr. Made in the USA.”
Post-1975 and later variants (including Titleist-only stamping and Scotty Cameron SC marks) reflect subsequent eras beyond Reuter’s original production.

Summary:


Original Bulls Eye putter production by John Reuter Jr.: approximately mid-1940s through the 1950s.
Acushnet/Titleist production under Reuter’s design: late 1950s through the 1960s and 1970s, with various marking changes.
Therefore, if you are referencing a classic John Reuter Jr. Bulls Eye SC putter, its earliest production roots trace back to about 1945, with trademarked and commercial production beginning in the late 1940s (circa 1949) and continuing into the 1960s/1970s depending on markings and manufacturer. "