Those 'clean' ones are often the worst, as the deck looks to be original. Amazing how Dual seemed to simplify the mechs as time went on, and they seemed to cycle more quietly too
Please persevere with it. I appreciate there's a couple of things needed which are different to the 1229 previous model, but they are related and the tonearm height adjustor is one of them that needs sorting - I wonder if this helps to mess up the positioning situation?
The infamous 'pimpel' is perhaps the most frustrating and the correct grease (Alvania? - from Mrow2 Don) in the correct proportion seems to be the way to go. Too much and the main lever friction surface is too slippery, too little and the new pimpel will be torn to pieces. I think the grease applied here is kind-of self limiting and a few cycles may be all you need to sort it out once correct adjustments are made. On the 1229 anyway, as well as others using this tonearm lifting arrangement, the little thumb-nut at the top of the cueing 'stud' assembly needs to be set properly, otherwise the lifting pin pushes the arm up hard on it's height restrictor and the arm effectively jams in one position. When the mechanism is manually cycled to lift the arm fully up, there should usually be a hairs breadth of free vertical tonearm movement before the arm contacts the max-height adjustor. I'm not good with words, and don't have a 1249 here, but look at fig 15 in the service manual and the lifting assembly '51.' The thumb nut is at the top with the arm height restrictor to the right of it and vaguely 'nut' shaped...
As Tinkaroo said, a lovely old deck and well worth fettling as a top notch auto deck, even just for single records. Auto-changing 7" singles can be fun as well and a more tolerant cartridge is a boon for this here (I use a Rega Carbon, which is a posh AT91, tracking at 1.8g, as it has a good conical tip which is less critical of tonearm VTA as this changes with the stack height and it's a great match to these Dual tonearms)