The fine tuning of the Simplex LJ 1000 rear derailleur and the SJA 102 front derailleur is a fairly straight forward procedure. If you removed the derailleurs from the bike and did nothing to them except clean and the lightly lube them, then this step will go very easily.
I am assuming that both derailleurs have been returned to their pre-restoration locations on the bike as described in restoration previous steps. If so, the SJA 102 front derailleur should have its cage parallel to the face of the outer chain ring and be located about 2 mm to 4 mm above the chain ring teeth. The rear LJ 1000 should be hanging on the rear dropout tab and be able to move freely on that tab. Both should have the Sedisport chain threaded through them and then over the largest rear cog and the larger of the two front chain rings. This gear combination (big/big) is never used in the real world because of the extreme cross chaining involved which accelerates chain noise as well as wear on the chain, cogs and outer chain wheel. The reason you use this as the default location for setting the derailleurs is that the system must be able to accommodate this maximum length of the chain in case the gear combination is engaged inadvertently. If this configuration cannot be adopted because you have changed to a larger freewheel or a new chain or both, you must lengthen the chain to accommodate this arrangement. Failure to permit the system to engage the big/big configuration will result in difficulty shifting onto the big cog or an inability to shift onto the big chain ring. It’s the old story: change one thing, change many.
However, if all you have done is clean and lube and resisted the urge to fiddle with the derailleurs while off the bike, the next steps are straight forward as promised earlier. It is critical to be sure the inner and outer throw of the front and rear derailleurs are accurate. If you get the rear derailleur adjustment wrong, you can stuff the derailleur into the spokes destroying the wheel, the derailleur and possibly even bending the rear dropout and frame as well. If you permit over shifting at the front, the chain may land on the crankset gouging the finish. Worse, the chain could go between the crank arm and the spider jamming and gouging up that side.
For the rear derailleur, you will need to use the adjusting screws on the derailleur body to adjust the inner and outer throw of the derailleur. The upper screw controls the outward throw of the derailleur to access the high gear cog. The lower screw controls the inward range of the derailleur throw to allow low gear engagement. To check the set of the derailleur range put the right Retrofriction all the way forward. Manually place the chain on the smallest cog. Turn the cranks and pull the gear lever back, sequentially selecting the next cogs. As you approach the largest cog, be careful of the force you apply to the lever and select the largest cog. There should be no extra travel available which would allow over shifting the chain into the spokes. If travel is still available, use a small straight blade screwdriver to screw outward the upper travel screw. This limits excess motion and prevents disastrous overshifting into the spokes. Carefully re-try and test that the throw limit is correct.
Turning the cranks, shift back down the 6 cogs of the freewheel until you cautiously approach the smallest, high gear cog. As above, if the cog engages without extra lever motion available, you are fine. If lever motion is still available, use the straight bladed screwdriver to screw the limit screw inward to prevent over shifting. Once the limits are set, it may be necessary to re-tighten the derailleur shift cable to eliminate slack.
To check the front derailleur throws, set the chain on a middle cluster cog. Using the left Retrofriction lever , carefully turn the pedals and gently pull the lever back. The chain should climb onto the big chain ring. If lever travel remains, use the straight blade screwdriver to move down the screw limiting extra movement. Carefully turn the cranks and then gently move the left Retrofriction lever forward to derail the chain off the big ring. The chain should drop neatly onto the small ring with just enough extra lever movement to allow the front derailleur cage to clear the chain as the chain goes up the cluster and onto the big cog on the freewheel. If excess motion remains at the lever, use the screwdriver to screw down the inner travel limit screw to prevent the chain from derailing onto the bottom bracket shell or jamming between the inner chainring and the axle. Any excess cable slack should be removed if this adjustment was necessary.
Once you have completed all the basic adjustments while on the work stand, run the shifts up and down the cluster gradually increasing the loads and the speeds of the shifts. The derailleur should shift quickly and cleanly from low gear to high, up and down the freewheel cluster with no overshifts beyond the cogs. Do the same for the front chainrings. Then take the small screwdriver with you and one large enough to fit the Retrofriction screw and ride the bike outside or on a mag trainer. Run the same upshift/downshift tests you did on the work stand paying special note to the possibility of Retrofriction lever slippage under load such as sprinting. Tighten and fine tune as necessary. Once the Retrofriction lever tension is set, it should stay that way until or if you choose to change it. Watch after the first few rides and check shift lever cable tension. There may be some stretch and you may have to remove that from the cables to keep the shifting smooth and linear.
One further step needs to be taken. After test riding the PB 12, I noticed cracking in the Michelin TS sidewalls which is quite typical of Michelins in general. However, there were also cracks in the tread which, upon higher pressures and closer observation, were observed to extend down to the fibers of the tire carcass. Replacement of the tires was obviously going to have to happen next.