I've been using an assortment of Neodymium magnets on Lugol's 5% 25 mL bottles.
Various sizes, 2" x 1" x 1/4" or 1/2" thick.
Also 50 x 25 x 10mm all using a variety of prototype 3D printed Magnet Holders.
Pull strengths from about 40 lbs to about 90 lbs.
Very satisfactory and convenient arrangement, much much safer than taping or attaching these magnets directly to bottles.
Magnetized Iodine seem to almost eliminate the Iodine taste... as others on this forum report.