Using laser-induced phetodetachment (LIPD), we investigate in some detail how different discharge parameters affect the negative ion fraction in high-density low-pressure SF6 magnetoplasmas sustained by the propagation of electromagnetic surface waves. A plane electrostatic probe is used for collection of the photodetached electrons. Careful testing of the LIPD technique itself is carried out prior to systematic measurements and adequate laser fluence conditions are determined. Negative ions are found to outnumber electrons several times, even at mTorr and submTon pressures, indicating the important electronegative character of the discharge. The dependence of the negative ion fraction on gas pressure, argon admixture, microwave power, and axial and radial position in the reactor is interpreted on the basis of different negative ion formation and loss mechanisms. The negative ion fraction is found to be maximum in conditions and regions of minimal electron temperature and positive ion density.