Driver visual distraction due to the prevalence of mobile phone engagement has become a major safety concern for transport authorities worldwide. Despite long-term efforts to prevent engagement in mobile phone tasks, drivers continue to use their phones while driving. To develop better policy and prevention practices, gaining an understanding of the predictors and strategies utilised by drivers who use their mobile phone for distracting tasks is necessary. Visually intensive tasks are the main interest of this investigation, e.g., texting and browsing. In an online-questionnaire in Queensland (Australia), of the 484 drivers who participated, a 33.5% (n = 162) of respondents reported using a mobile phone for texting and browsing while driving on a typical day. Answers from these participants were analysed for this study. Negative binomial regression was used to model the effect of the independent variables (personal characteristics, perceived crash risk, beliefs, workload management strategies, and police avoidance strategies) over the rate of texting/browsing events per hour driving. The final statistical model confirmed that drivers who reported previous collisions; who believed that the effects of doing the texting/browsing task would last after it was finished; and who reported keeping their phone low to avoid police had an increased texting/browsing incidence rate. Comparably, drivers who held a valid driving license for longer; who perceived larger crash risk regarding texting/browsing behaviour; who avoided mobile phone use in demanding driving conditions; and who used workload management strategies such as reduced speed when engaged in mobile phone use had a reduced texting/browsing incidence rate. The results provide insights into the limitations of actual enforcement control and potential opportunities for countermeasures.