Well, not perfectly sure about the meaning, but judging from the lyrics which deal with the usual pining over unrequited love in high school, I think "Toiki de Net"may mean "Net Him With A Sigh", perhaps the aidoru romantic version of the fisherman's "Caught Me A Marlin!".
In the latter half of the 80s, I was diversifying away from just listening to aidoru and other residents of the Top 10 lists, so I never became a hugely devoted fan of some of the young singing starlets during that time, but Minamino's 11th single has been a song that has stayed with me over time. Written by Jun Taguchi（田口俊）and composed by Toshihiko Shibaya（柴矢俊彦）, "Toiki de Net" is a sunny aidoru tune with that little splash of Latin flavour....a bit like an aidoru version of a Rum and Coke (real Coke, not the Diet one). The song was released in February 1988, so I gather that the song provided some nice summery-ness during that Winter.
"Toiki de Net" was Minamino's 6th of 8 straight No. 1 hits, and this one became the most successful hit of her career since her debut in 1985, selling 300,000 copies. It eventually became the 11th-ranked song of the year.
As for Nanno, she originally came from Hyogo Prefecture before moving up to Tokyo, where she attended the celeb-rich high school, Horikoshi High. Her grademates included fellow aidoru Minako Honda and Yukiko Okada. Of course, she has also seen success on TV as an actress, starring in the 80s as the second of the teenage yoyo-twirling super sleuths (after Yuki Saito) in the "Sukeban Deka"（スケバン刑事....Delinquent Girl Detective) franchise, although it's hard to imagine to either see Nanno or Saito shoplifting dust from a store. Currently, she's still appearing on the tube as a regular TV personality, and I just caught her on an NHK show learning how to make French pastries from a chef. Has barely aged a year.