Photoneutron reactions were investigated for the deformed ${}^{165}$Ho and ${}^{169}$Tm nuclei from the vicinity of the neutron emission threshold up to $$40~MeV, well above the giant dipole resonance (GDR) region, using quasimonochromatic laser Compton scattering $\gamma$-ray beams provided at the NewSUBARU facility, Japan. A high-and-flat efficiency moderated array of ${}^3$He counters was used for the neutron detection and an associated neutron multiplicity sorting method for extracting the $(\gamma ,1nX)$, $(\gamma ,2nX)$, $(\gamma ,3nX)$ and $(\gamma ,4nX)$ reaction cross sections and average neutron emission energies. The present ${}^{165}$Ho cross sections were compared to existing data, revealing discrepancies with the Saclay multiplicity sorting results and an overall 10$\%$ strength difference with the Livermore ones. There are no other data for ${}^{169}$Tm. The total photoneutron cross sections $\sigma (\gamma ,Sn)$ were determined by summing the partial $(\gamma ,inX)$ components. GDR parameters based on phenomenological Lorentzian models were extracted by fitting the present $\sigma (\gamma ,Sn)$ data with adjustments for the missing contribution of charged-particle-only reactions not observed experimentally. For both nuclei we observed high energy structures at 20-25~MeV, matching giant quadrupole resonance predictions from the microscopic Kombined Model of Fotonuclear Reactions (KMFR). Based on the present centroid energies of the first and second GDR peaks, hydrodynamic model predictions gave intrinsic electric quadrupole moments of +7.00(34)~b and +7.38(28)~b for the ground states of ${}^{165}$Ho and ${}^{169}$Tm, respectively. The present experimental excitation functions and photoneutron energies were compared to statistical model calculations. Using the EMPIRE statistical model code, we performed a sensitivity test to phenomenological models of photon strength functions and nuclear level densities. The TALYS code was used to reproduce the present experimental $(\gamma ,inX)$ cross sections and average neutron energies using microscopic nuclear level density models.