From 11,060' in Bilk Basin, put any maps you have away. They will steer you wrong as nearly all maps of this region show the Lizard Head Trail incorrectly from this point. Your eyes will be your best guide. It may be helpful to study this area using satellite views on Google Maps to orient yourself correctly.
From the last trees, the trail drops slightly and crosses a brief area of rock as it lowers closer to the stream. Do not cross the creek, as most maps show. Instead, the trail stays on the north side of the creek as it begins switchbacking up the south slopes of Wilson Peak toward a small lake at 12,063'. In high snow years or early season, this part of the trail may be covered in snow. If that's the case, pick your best line somewhere to the right of the main drainage as you make your way up toward the bench with the small lake.
From the lake, the best route in snowy conditions will be to gain the north ridge of Gladstone as high as possible to eliminate as much of the ridge scramble as possible. To do so, leave the trail (if you were ever on it) and cross to the other side of the creek/lake. To your left (southwest) there will be a broad ridge descending from Gladstone's north ridge that splits Bilk Basin in half. Aim for a broad, low point in this ridge around 12,600'.
From the broad ridge, survey Gladstone's north ridge and pick your entry point. The terrain nearest the to lowest saddle is generally the least steep. In a high snow year or early season, you may opt to gain the ridge crest even closer to the summit if snow conditions permit by following the snow field up to the ridge crest at any number of reasonable points. Using crampons and ice axes in the record snow year of 2019, we were able to gain the ridge proper at about 13,400'.
Once on the ridge, follow the crest as closely as possible to the summit. The ridge is tedious, loose, and exposed. Test every hold. When necessary, bypass obstacles on the crest by navigating terrain close to the crest on the east (left) side. It is not necessary to drop more than a few feet below the crest at any point on this section of the climb/traverse. Avoid any temptation to do so.
From the summit enjoy spectacular views of Mount Wilson and Wilson Peak. Carefully retrace your steps back to a safe exit point on the ridge and follow your ascent route for the return back to the trailhead.