The 1084 *does* have a degauss. There is a posistor [2322 662 98018] located at [R104] on the SMPS unit.
If you believe it *not* to be degaussing and intend to fault-find this is where you should start.
** Remember electricity KILLS. **
If you could post a photo of the affected 1084 monitor this would prove useful for determining exactly what is wrong with your screen before you proceed.
If you believe that it *has* been damaged by a speaker magnetic, degaussing will *not* necessarily fix this because the shadow mask NOW has an additional, possibly permanent, "magnetised" field in that affected area which is usually "stronger" than the CRT's own field. (Then you need a professional external device to do the job correctly.)
** The concept of degaussing is to randomised the entire field of the shadow mask preventing localised discoloration **
Many folk seem to get confused with the role of the degauss believing it is suppose to remove any magnetism; it doesn't. (requires more detailed explanation.)
I wouldn't explore the "magnet on a drill" nor "swap out just any degauss coil", it's crude.
CRTs are magnetically conditioned at the factory; this can include hemisphere orientation.
Any "manual" degaussing if done incorrectly will destroy the conditioning AND the purity of your CRT.
** Do not switch your 1084 on/ off repeatedly in an attempt to degauss the screen over n' over, the rapid succession of high current
may kill your coil/SMPS. **
Shifting:
* One method you made wish to explore with permanent damage or severe purity issues is placement of a disc magnetic of equal strength (generally fridge magnetic strength) but
opposite field orientation to "shift" the magnetism "away" from shadow mask; but this can be quite tricky. (see attached photo.)
** A common example of *dependency* of magnets to correct a CRT is the classic case of hifi speakers that have been either side of a CRT for so long that actually removing them causes the problem because of how the tube environment has changed over time. In other words the speakers need to remain!
You also need to keep in mind your shadow mask is an precision engineered perforated sheet of metal. Whacking a strong magnetic against
it could potentially warp it leaving you with a bigger problem of mal-alignment to the in-line electron beams converging on the phosphor.
Paul.
*Edit*
There's some useful information in the C= 1084 Service Manual available online as.pdf regarding static/dynamic convergence, B&W tracking, Colour purity, Degauss coil.