Even though it has been 2 months, as a Singaporean I must answer your question.
(For this post, abbreviations: SG = Singapore, SGean = Singaporean, M'sia = Malaysia, M'sian = Malaysian)
Sources vary on whether SG left on its own because of the PAP or whether M'sia's ruling party evicted Singapore. The common consensus, however, is that M'sia kicked SG out in 1965 and SG unwillingly left.
I arrived at this conclusion because of three things:
Singapore wanted to stay. Singapore's then-leader, Lee Kuan Yew, was very supportive of Singapore being a part of the M'sia. When SG separated from M'sia, Lee said on national TV: "For me it is a moment of anguish because all my life ... you see the whole of my adult life ... I have believed in merger and the unity of these two territories. You know it's a people connected by geography, economics, and ties of kinship ..." [1] This shows that Lee strongly believed in SG being a part of M'sia. Additionally, a majority of SGeans had voted to merge with M'sia in 1962 in the first place. [2]
Most of the then-SG government were unaware that the split was even going to happen and only the top levels of government in SG were aware that anything was happening. [3] Several other top-level SGean government officials, such as S. Rajatranam and Toh Chin Chye also refused to sign the separation agreement and only did so reluctantly after persuasion. [4]
M'sia had political interests in kicking SG out. UMNO, then-ruling party of M'sia, felt threatened by the SGean PAP because they felt the Chinese-dominated SG and PAP would act as an avenue for the subjugation of the Malay race in M'sia. [5] This was not helped when PAP ran in M'sia's federal elections and won a seat in the M'sian parliament in 1964. Thus, UMNO felt like it had to remove PAP, and by extension, SG as a threat. This sentiment that 'SG is a threat and needs to be neutralised' can be seen in the 9 August 1965 vote in the M'sian parliament, where M'sian PMs voted 126–0 in favour of the expulsion of Singapore, with Members of Parliament from Singapore not present.
Citations
[1] Lee, Kuan Yew (19 November 1961). "Transcript of Recorded Press Conference by the Prime Minister, Mr. Lee Kuan Yew, Broadcast over Radio Singapore at 7.10 p.m. on Sunday, November 19, 1961 [Singapore Government Press Statement MC. No. 74/61/TTS]" (PDF). Government of Singapore (archived on the National Archives of Singapore website). Archived from the original (PDF) on 9 August 2014. (An interview with the Prime Minister of Singapore regarding merger negotiations.)
[2] Singapore: An illustrated history, 1941–1984. (1984). p. 224.
[3] Turnbull, C. M. (2016). A history of modern Singapore, 1819-2005. Singapore: NUS Press. pp 293-294
[4] Lee, K. Y. (1998) The Singapore story : memoirs of Lee Kuan Yew. pp. 638–644.
[5] Singapore: An illustrated history, 1941–1984 (1984). p. 269; Cheah, B. K. (2002). Malaysia: The making of a nation.