In fact, it really was Kent Tekulve who brought back the nearly underhanded delivery, something that was very prominent in early baseball and through the 20th century. In fact, when baseball was in its infancy, pitchers were actually required to throw the ball underhand and were penalized if they threw a pitch overhand. The underhand pitching rule, which lasted through 1883 stated, "The ball must be pitched, not thrown, for the bat." "Pitched", in the traditional sense of the term: a stiff, underhanded motion, almost like bowling."
Once pitchers got the hang of throwing the ball overhand, and once it was legalized, there was little benefit in a pitcher throwing the ball sidearm. Several years went by before anybody pitched exclusively as a sidearm pitcher. Some underliers included Dick Hyde and Russ Christopher, among others. Pitchers like the before mentioned Tekulve, Dan Quisenberry, and Gene Garber had a lot of success in the 1970's and 1980's throwing sidearm.
The Mets had Terry Leach as well, a sidearm pitcher who pitched with the Mets in 1981 and 1982, then again for the team from 1985-1990. Leach, on many occasions, was used as a starting pitcher making 18 of his 176 appearances as a starting pitcher, three of them complete game shutouts.
The Mets of 1987 had a lot of things go wrong for them, the least of whom the hangover from winning the World Series the previous season. Dwight Gooden missed the start of the season due to being forced to enter a rehab center to avoid suspension after testing positive for the use cocaine. Injuries to Bob Ojeda and Rick Aguilera as well as an injury that cost Sid Fernandez 18 days led the Mets to use multiple starting pitchers during the 1987 baseball season. The Mets used twelve starters that season, seven of whom made at least twelve starts for the team. The Mets made a March 27th trade with the Royals to acquire David Cone, a May 11th deal for Indians pitcher Don Schulze, then a September 15th trade for Angels left-handed pitcher John Candelaria.
On May 26, 1987, the Mets were set to play the San Francisco Giants during the first leg of their three team, West Coast trip. A day before, the Mets won the opener of the series 8-7 over the Giants in a game started by John Mitchell, who at the time, was only the sixth different starting pitcher for the Mets that season. Gooden had not yet started a game and Bob Ojeda was already on the Disabled List (now referred to as the Injured List). Sid Fernandez was in the process of skipping a start due to an unknown ailment. The Mets would call on a relief pitcher who had only made two appearances in the big leagues to make the spot start.
Jeff Innis would give the Mets as much, if not more, than they could have imagined as he pitched four innings, giving up just two runs, seven hits with three strikeouts while giving up a solo home run to Will Clark. The Giants led the game 2-1 going into the top of the eighth inning. Jeff Robinson was pitching for the Giants in his second inning of relief. He gave up a single to Keith Hernandez before walking Darryl Strawberry to start the inning. After a Mookie Wilson infield single loaded the bases, Giants manager Roger Craig (himself a former Mets pitcher) went to ace reliever Scott Garrelts, who promptly threw a wild pitch allowing the tying run to score and moving the other two runners into scoring position. Garrelts struck out Howard Johnson and Barry Lyons before uncorking another wild pitch to score Strawberry to give the Mets a 3-2 lead. After striking out Rafael Santana, the box score would make it seem as if the Giants relief ace did his job by striking out all three batters he faced. The two wild pitches turned out to be the difference in the game as the Mets held on for a 3-2 victory with Jesse Orosco pitching the ninth to earn the save for Doug Sisk, who pitched the eighth inning. For the record, Randy Myers pitched scoreless fifth and sixth innings for a Mets bullpen who kept the Giants off the board for all four innings they were in the game.
Innis' next 285 appearances for the Mets would all come in relief, the last of whom was on October 3, 1993. He pitched in the minors for the Twins, Padres, and Phillies before walking away from the game after the 1995 season. He should have earned some more big-league time during the 1987-1990, earning 14 wins and 38 saves in 128 appearances while pitching for the Triple- A Tidewater Tides. The Mets had a deep bullpen for the majority of those seasons, and it was tough for Innis to get a lot of big-league work. Plus, I bet the Mets felt Innis as a side arming pitcher was redundant since they already had Leach in the bullpen. Innis' start in 1987 was the only one he ever made as a professional pitcher.
For the heck of it, here is a list of some other post 1980 side arming pitchers-
Steve Olin (RIP)
Any more not mentioned, please add to the comment section.