I remember hearing of this when Byron White retired in '93. He had been appointed by a Democrat : JFK. He never really changed his politics much in his 30+ years on the USSC, which meant that the extreme leftward lurch of the Democrats during those decades had the effect of redefining White from conservative to liberal.
You might remember him as the dissenter on Roe v Wade who correctly and bitingly described it as "an exercise in raw judicial power".
But even though he had much, much more in common with Republicans than with Democrats by 1990 when he was about ready to retire, he purposely delayed his retirement while the GOP was still in the White House, and waited until just after Clinton took office. Even though a Republican-appointed Justice would have been much more in tune with his judicial philosophy, he remained true to the old traditional "honorable" way of doing things, and retired during a Democrat administration.
And a few years before that, Democrat Justice Thurgood Marshall attempted to do the same. (Although it's unclear whether he did this out of a sense of honor, or because he had lurched leftward with the post-60s Democrats and desperately wanted to be replaced with someone of his same persuasion). But the Democrats remained in the wilderness outside the White House walls for so long - 12 years to be exact - that Marshall's health made it impossible for him to outlast Reagan and GHW Bush.
So now, let's look at J. P. Stevens. He was appointed by a Republican - Nixon. This means that following the honorable old tradition would require him to attempt to retire during a GOP Presidency. He's had that chance for the past 8 years. What do you think are the odds that he either plans to retire in the next 2 months, or to outlast the upcoming Democrat reign?
It’s interesting that Byron White almost didn’t end up on the court at all. JFK was intending on naming the first Black to the court in 1962 and had settled on former Virgin Islands Governor and federal Judge William Hastie. Hastie had actually been Thurgood Marshall’s law professor. But Hastie was actually a judicial Conservative and faced opposition from two fronts. Southern Democrats would be damned to see a Black on the court, and Earl Warren would be damned to see a Conservative, so Hastie was put on the back burner and White got the nod. JFK was going to slip Hastie in at some point in the future, but with his assassination, he was forgotten and LBJ appointed far more moonbattier appointees, including Marshall (who was, of course, a perfectly fine and successful lawyer, but absolutely execrable jurist who brought a set agenda to the court on par with the equally dreadful Earl Warren, the worst SCOTUS Chief in the history of the country). President Ford would’ve gotten a second appointee on the court had Hastie served until his death in 1976 who more than likely would’ve been a Stevens clone.
When Nixon won the '68 Presidential election, "Republican" Justice Earl Warren did the opposite and quickly submitted his resignation so the lame duck Democrat President (Lyndon Johnson) would be able to replace him with another activist liberal. Johnson attempted to do an 11th hour elevation of Abe Fortes from Associate Justice to Chief Justice and it didn't work. Fortes came off as arrogant and trying to seize power, and the Republican minority just held up the nomination until Nixon could be sworn in and appoint his own guy.
IF John Paul Stevens decided to resign at this time so a Republican President would name his replacement (won't happen since Stevens is a lib), the same scenario would probably unfold. Bush would attempt to name a conservative, and the Dems would drag their feet for two monthes and hold up the appointment until Obama can be sworn in and name his own judge.