Could be a number of causes.

Is the tailstock centre in good condition?

Is it cleanly mounted in taper?

Last and by no means least, how did you drill the centre for in the aluminium material?

I would suggest that the point of the tailstock centre isn't quite central.

Several possible reasons, tailstock itself not central, barrel wear allowing clamp to offset barrel in tailstock casting, a bit of debris in the morse taper bore, or between tailstock and bed tilting it over, slightly bent running centre spindle; I'm sure there are others.

How to find out which is harder;
Maybe the following. Do you have a dial gauge? if so set it up in the toolholder.

Edit, Sorry just realised you are using a chuck at the headstock end;
You already have a long bar which appears to be tapered, so zero the clock on that bar, at the headstock end on a portion you have just turned to size (any size).

Try turning a bar between centres and see if the error repeats. If so then move carriage to tailstock end observing the clock; since you've already turned the bar between centres, using those settings, the needle should barely move.
Leaving the same settings on the toolpost, reverse your workpiece; I presume the clock will now give a different reading due to the different diameter. Keep the same settings and investigate how each of the above causes a change in that reading.
i.e. loosen and tighten tailstock clamp, barrel clamp, slightly rotate running centre body, and then full 180° etc.
Replace running centre with a plain one, clean taper etc. This should hopefully point to where the tailstock centre offset is being generated.

Further to that, if nothing immediately shows, then the tailstock casting centre line might be off, which is adjustable as you know. If there is a need to make a new bar perfectly parallel, and the same length, then you already have the correct setting on your clock gauge. Using the tailstock offset screws adjust it so the clock reads zero.
This should be repeatable for your new workpiece, but perhaps only for this exact length.
 

Alternatively if you need various pieces, you could always use an MT2 boring head with a centre in it, so you can dial in an offset, much like turning a taper; in this case it's just a parallel taper. 

In my case I made a dead centre for the boring head using a broken carbide centre drill.

Bill

Edited By peak4 on 23/12/2019 12:02:55

Edited By peak4 on 23/12/2019 12:07:24

I never expected such a long link, still, it works.

.

I’ve mentioned this before, but ebay still keeps catching us out

Everything from the question mark onwards is superfluous to our needs

… it’s all ebay tracking how you reached the page.

MichaelG.

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Demonstration:

This should link to exactly the same page

https://www.ebay.co.uk/itm/2MT-Lathe-Alignment-Test-Bar-MT2-Alloy-Steel-Over-All-Length-283mm-11-1-8-Inch/174007649507

Edited By Michael Gilligan on 23/12/2019 17:50:13

Personally, I'd use a bit of bar held in the chuck and turned to a 60° taper.

That way it's guaranteed to be concentric with the spindle rotation. Keep it, but re-turn the taper each time you re-mount it.
It does leave more overhang from the headstock, but this might be an advantage as none of the saddle will be overlapping the gap part of the gap-bed. Also it provides a drive dog for your right angled driver; that is you use one of the jaws to drive the workpiece when turning between centres.
Also depending on the length and shape of the workpiece, swapping between 3 and 4 jaw chucks allows you to move the actual point of the home made centre along the lathe bed a bit. (Myford independent 4 jaws are often shorter than 3 jaw self centring chucks.)

Bill

Edited By peak4 on 23/12/2019 18:25:13

You would be best to turn the soft centre to get the alignment done, but putting a dead centre in the spindle taper and repeating the tests would be an excellent check of consistency. The freshly turned soft taper absolutely guarantees alignment with the spindle axis, until you remove of course. I keep the shank of a bolt for exactly this purpose, and reskim the taper before testing. When I bought the test bar, I made the mistake of using a live centre in the tailstock, and what I got was the runout of the centre. changing to a dead centre, and turning the test bar in it proved that the centre in the bar was good, I got zero detectable runout. The test bar in the advert is cheap enough and has the added advantage of having the Morse taper built in. It can also be used in the mill spindle and in the appropriate size collet for testing and alignment.