Nonlinear magnetic errors in low-beta insertions can have a significant impact on the beam-dynamics of a collider, such as the CERN Large Hadron Collider (LHC) and its luminosity upgrade (HL-LHC). Indeed, correction of sextupole and octupole magnetic errors in LHC experimental insertions has yielded clear operational benefits in recent years. Numerous studies predict, however, that even correction of nonlinearitites up to dodecapole order will be required to ensure successful exploitation of the HL-LHC. It was envisaged during HL-LHC design that compensation of high-order errors would be based upon correction of specific resonances, as determined from magnetic measurements during construction. Experience at the LHC demonstrated that beam-based measurement and correction of the sextupole and octupole errors was an essential complement to this strategy. As such, significant interest also exists regarding the practicality of beam-based observables of multipoles up to dodecapole order. Based on experience during the LHC's second operational run, the viability of beam-based observables relevant to dodecapole order errors in the experimental insertions of the HL-LHC are assessed and discussed in detail in this paper.