Previous edit was while on the move, but here are some quotes. Note that after the 1990s, the topic is largely ignored so as not to attract attention to the (apparently controversial) issue:
Insight, vol. 2, p. 362:
Those for Whom Christ Is Mediator. The apostle Paul declares that there is “one mediator between God and men, a man, Christ Jesus, who gave himself a corresponding ransom for all”—for both Jews and Gentiles. (1Ti 2:5, 6) He mediates the new covenant between God and those taken into the new covenant, the congregation of spiritual Israel. (Heb 8:10-13; 12:24; Eph 5:25-27) Christ became Mediator in order that the ones called “might receive the promise of the everlasting inheritance” (Heb 9:15); he assists, not the angels, but “Abraham’s seed.” (Heb 2:16) He assists those who are to be brought into the new covenant to be ‘adopted’ into Jehovah’s household of spiritual sons; these eventually will be in heaven as Christ’s brothers, becoming a part with him of the seed of Abraham. (Ro 8:15-17, 23-25; Ga 3:29) He has transmitted to them the promised holy spirit, with which spirit they are sealed and are given a token of what is to come, their heavenly inheritance. (2Co 5:5; Eph 1:13, 14) The total number of those who are finally and permanently sealed is revealed in Revelation 7:4-8 as 144,000.
Insight, vol. 2, p. 858:
Moses prophetically foreshadowed Jesus Christ, the great Mediator for anointed Christians, as they approach heavenly Mount Zion.
The Watchtower, 15 January 2015, p. 16:
Jesus is the Mediator of the new covenant, and loyal anointed ones taken into it receive a heavenly inheritance.
The Watchtower, 1 September 1996, p. 14:
This small, spirit-anointed group of Christians would later be joined by “a great crowd” from all nations who would also seek to worship Jehovah. (Revelation 7:9, 10; Zechariah 8:23) While not party to the new covenant, these too would be bound by law.
The Watchtower, 15 August 1989, p. 30–31:
Questions From Readers
□ Is Jesus the Mediator only for spirit-anointed Christians or for all mankind, since 1 Timothy 2:5, 6 speaks of him as the “mediator” who “gave himself a corresponding ransom for all”?
[Entire article; short answer, yes.]
The Watchtower, 1 January 1985, p. 19:
Jesus Christ is the Mediator of the new covenant and anointed Christians in it are called to inherit the Kingdom.
The Watchtower, 1 April 1979, p. 31:
Questions From Readers
● Is Jesus the “mediator” only for anointed Christians?
[Entire article; short answer, yes.]
Of course, it can't be demonstrated that any of this is actually
real, so it's not worth worrying about too much. But it is certainly the case that JWs officially believe that Jesus is mediator (at the very least, in some 'fullest sense') to only the 'anointed'.