Yes...adjust the screw in the link to the auto spindle operating pawl so that it engages positively over its entire travel. The pawl should push a record off, then reverse its stroke so it pushes backwards, thus " feeling" whether there is a record to be played on the NEXT cycle. Note that this sequence on your SL95B differs from that on the GT models, which "sense" the presence or absence of a record at the START of the cycle rather than at the end as on the "big SL" and Zero models.
Also make sure the Stop Lever, on the right side of the chassis under the platter, is free to move and is not stuck or stiff to move. It is an "overcenter" lever: when pushed halfway with your finger, its spring should push it the rest of the way with no further assistance.